Iterative Method

Barron. R.M. and R.K. Naeem. 2-D transonic calculations on a flow-based grid system. Mathematics and Computers in Simulation 33 (1991) 65-67. Lifting transonic full-potential flow is investigated using a streamfunction formulation which combines grid generation and flow physics into a single equation for the transformation metric. Supercritical calculations are carried out using the modified density method to provide numerical dissipation. The formulation is inherently simple and leads to easy coding and efficient computation.

One of the most important problem for solving the linear system Ax = b, by using the iterative methods, is to use a good stopping criterion and to determine the common significant digits between each corresponding components of computed solution and exact solution. In this paper, for a certain class of iterative methods, we propose a way to determine the number of common significant digits of x m and x, where x m and x are computed solution at iteration m and exact solution, respectively. By using the CADNA library which allows us to estimate the round-off error effect on any computed result, we also propose a good stopping criterion which is able to stop the process as soon as a satisfactory informatical solution is obtained. Numerical examples are used to show the good numerical properties.

Results of ongoing work in developing methods for performing multi-sensor fusion for the purpose of locating unexploded ardnance in shallow water and creating models of the seafloor for visualization are presented. The sensor suite includes a forward-looking sonar, a low frequency side-looking sonar, a high frequency side-looking sonar, a magnetic field gradiometer, and an electro-optic laser-scanning sensor. Data fusion techniques discussed include an iterative method of performing automatic target recognition processing (ATRP) on individual sensor channels, correlating the individual sensor channels for ,a single pass using the target locations to assist the process, performing correlations on multiple passes over the same target area, and returning the correlated data to the ATRP algorithms. The second pass of the ATRP algorithms on the correlateld data provides an additional method for locating and identifyiing targets while rejecting clutter. The focus is on the multi-sensor correlation and fusion techniques rather than the ATRP algorithms. Correlated sensor data, along with GPS information, is used to create three-dimensional models of the sea floor. The sea-floor models are used for visualization of the area around an item of unexploded ordnance to assist in planning remediation of the site. Fusion of multi-sensor data, and the production of models of the sea floor, are important capabilities for autonomous underwater vehicles. The models can be used for autonomous vehicle navigation and operation while the d,ata may be transmitted to a base station for additional analysis purposes.

This paper considers the use of punctured quasiarithmetic (QA) codes for the Slepian-Wolf problem. These entropy codes are defined by finite state machines for memoryless and first-order memory sources. Puncturing an entropy coded bit-stream leads to an ambiguity at the decoder side. The decoder makes use of a correlated version of the original message in order to remove this ambiguity. A complete distributed source coding (DSC) scheme based on QA encoding with side information at the decoder is presented, together with iterative structures based on QA codes. The proposed schemes are adapted to memoryless and first-order memory sources. Simulation results reveal that the proposed schemes are efficient in terms of decoding performance for short sequences compared to well-known DSC solutions using channel codes.

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut

Leveraging the power of nowadays graphics processing units for robust power grid simulation remains a challenging task. Existing preconditioned iterative methods that require incomplete matrix factorizations can not be effectively accelerated on GPU due to its limited hardware resource as well as data parallel computing. This work presents an efficient GPU-based multigrid preconditioning algorithm for robust power grid analysis. An ELL-like sparse matrix data structure is adopted and implemented specifically for power grid analysis to assure coalesced GPU device memory access and high arithmetic intensity. By combining the fast geometrical multigrid solver with the robust Krylov-subspace iterative solver, power grid DC and transient analysis can be performed efficiently on GPU without loss of accuracy (largest errors < 0.5 mV). Unlike previous GPU-based algorithms that rely on good power grid regularities, the proposed algorithm can be applied for more general power grid structures. Experimental results show that the DC and transient analysis on GPU achieves more than 25X speedups over the best available CPU-based solvers. An industrial power grid with 10.5 million nodes can be accurately solved in 12 seconds.

In this paper, we empirically investigate the NP-hard problem of finding sparsest solutions to linear equation systems, i.e., solutions with as few nonzeros as possible. This problem has received considerable interest in the sparse approximation and signal processing literature, recently. We use a branch-and-cut approach via the maximum feasible subsystem problem to compute optimal solutions for small instances and investigate the uniqueness of the optimal solutions. We furthermore discuss five (modifications of) heuristics for this problem that appear in different parts of the literature. For small instances, the exact optimal solutions allow us to evaluate the quality of the heuristics, while for larger instances we compare their relative performance. One outcome is that the so-called basis pursuit heuristic performs worse, compared to the other methods. Among the best heuristics are a method due to Mangasarian and a bilinear approach.

This paper presents an iterative method for the computation of approximate solutions of large linear discrete ill-posed problems by Lavrentiev regularization. The method exploits the connection between Lanczos tridiagonalization and Gauss quadrature to determine inexpensively computable lower and upper bounds for certain functionals. This approach to bound functionals was first described in a paper by Dahlquist, Eisenstat, and Golub. A suitable value of the regularization parameter is determined by a modification of the discrepancy principle.

The global optimization of sensor locations and a sensitivity analysis based on the minimization of interferences due to wireless communications between sensors are studied in the presence of additive white Gaussian noise (AWGN). We used a Gram matrix approach for robust determination of sensor locations by minimizing the interferences (maximizing the signal strength) among sensors for engine health monitoring systems. In order to solve the problem of optimum placement, an iterative algorithm for maximizing the determinant of the Gram matrix is proposed and implemented. The sensitivity criterion proposed in this paper is the spectral number of the Frobenius norm of the Gram matrix associated with sensor readings. We derived the necessary conditions under which the number of sensors and the optimal sensor locations will remain unchanged when the data measured for sensitivity analysis is affected by AWGN. Our theoretical results are verified by simulations providing details concerning numerical implementations.

Solving linear system with a magnitude of thousand to ten thousand of unknowns takes a very long time in serial fashion. Furthermore, linear system that is discretised from Partial Differentiation Equations (PDE) is also typically solved by a class of iterative method. Therefore, by parallelising Jacobi Iterative Method using OpenACC, we are able to review and compare OpenACC’s capabilities in accelerating Jacobi Iterative Method using compiler directives approach as opposed to CUDA’s approach. Moreover, we implemented OpenACC in two distinctive domains, where the first domain is on manycore environment with a testbed hardware of Nvidia GeForce GTX 980 and the second domain is on multicore environment where 4 CPU(s) of AMD Opteron 6272 chips are clustered on a single machine with a total of 64 cores. This research project has shown great potentials of the implemented Jacobi Iterative Method using OpenACC as we managed to obtain verily rewarding results. Where, the highest speedup gain is up to 82x faster on GPU with Unified Memory (UM) enabled and 55x times faster on CPU where all 64 cores are fully utilized, and this is when the number of unknowns to be solved is 25,000 and 2,500 respectively.

This paper describes a method developed to evaluate the seismic performance of old masonry buildings, which allows identifying the expected structural collapse mechanism of the structure. The collapse mechanism is identified by the accumulation of several damaged ...

In this paper, we have combined the ideas of the False Position (FP) and Artificial Bee Colony (ABC) algorithms to find a fast and novel method for solving nonlinear equations. Additionally, to illustrate the efficiency of the proposed method, several benchmark functions are solved and compared with other methods such as ABC, PSO and GA.

The proposed contribution deals with the methods for the railway wheel and rail head profiles development on the base of the intended shape of wheelset/track contact geometric characteristics. The profiles creation method through arcs radii profile variation is explained, as well as the emphasis is directed to the "Iterative method for a railway wheel tread profile design". This method is explained in a more detailed way in the article. The base for the creation of new profiles with the help of the first method is an interactive attitude based on the modification of the original shape which is defined by section of a railway wheel profile, with interconnected and exactly defined arcs radii. It is possible to change them, according to shape needs of the final geometrical characteristics. The base of the iterative method, which is of the highest importance in this article, is to develop a new profile under given conditions-a prescribed shape of the contact points distribution and the shape of Delta-r function. The newly developed wheel profile in the couple with given rail profile will have the requested chosen characteristics shapes. This method can be after modification used for a design of rail profile in accordance to the wheel profile.

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut

We generalize the Guyan condensation of large symmetric eigenvalue problems to allow general degrees of freedom to be master variables. On one hand useful information from other condensation methods (such as Component Mode Synthesis) thus can be incorporated into the method. On the other hand this opens the way to iterative re nement of eigenvector approximations. Convergence of such a procedure follows from the result, that one step of (static) condensation is equivalent to one step of inverse subspace iteration. A short outlook on several applications is included. Zusammenfassung Durch eine Verallgemeinerung der Guyan Kondensation gro er symmetrischer Eigenwertprobleme wird die Verwendung allgemeiner Freiheitsgrade als Master-Variable erm oglicht. Dadurch k onnen einerseits Ansatzvektoren aus anderen Kondensationsmethoden in die Guyan Kondensation eingebunden werden, und andererseits werden damit gewonnene Eigenvektorapproximationen iterativ verfeinerbar. Die Konvergenz einer solchen Verfeinerung folgt aus dem Resultat, da die (statische) Kondensation als ein Schritt der inversen Unterraum Iteration interpretiert werden kann. Ein kurzer Ausblick auf Anwendungsgebiete schlie t die Arbeit ab.

The notion of a kth iterated Kiefer process ν t k for k ∈ and ν t ∈ is introduced. We show that the uniform quantile process β n t may be approximated on [0, 1] by n −1/2 n t k , at an optimal uniform almost sure rate of O n −1/2+1/2 k+1 +o 1 for each k ∈. Our arguments are based in part on a new functional limit law, of independent interest, for the increments of the empirical process. Applications include an extended version of the uniform Bahadur-Kiefer representation, together with strong limit theorems for nonparametric functional estimators.

This article proposes an original method for grading the colours between different images or shots. The first stage of the method is to find a one-to-one colour mapping that transfers the palette of an example target picture to the original picture. This is performed using an original and parameter free algorithm that is able to transform any N-dimensional probability density function into another one. The proposed algorithm is iterative, non-linear and has a low computational cost. Applying the colour mapping on the original picture allows reproducing the same 'feel' as the target picture, but can also increase the graininess of the original picture, especially if the colour dynamic of the two pictures is very different. The second stage of the method is to reduce this grain artefact through an efficient post-processing algorithm that intends to preserve the gradient field of the original picture.

We introduce the concept of a Markov risk measure and we use it to formulate risk-averse control problems for two Markov decision models: a finite horizon model and a discounted infinite horizon model. For both models we derive risk-averse dynamic programming equations and a value iteration method. For the infinite horizon problem we develop a risk-averse policy iteration method and we prove its convergence. We also propose a version of the Newton method to solve a nonsmooth equation arising in the policy iteration method and we prove its global convergence. Finally, we discuss relations to min-max Markov decision models.

In this paper, we present a new modification of Newton method for solving non-linear equations. Analysis of convergence shows that the new method is cubically convergent. Per iteration the new method requires two evaluations of the function and one evaluation of its first derivative. Thus, the new method is preferable if the computational costs of the first derivative are equal or more than those of the function itself. Its practical utility is demonstrated by numerical examples.

A hitherto unavailable nonlinear resonance (eigenvalue) based semi-analytical solution technique for prediction of the elastic mode 2 collapse pressure of a moderately thick cross-ply ring, weakened by a modal or harmonic type imperfection, is presented. A von Karman type iterative nonlinear analysis, that is based on the assumptions of transverse inextensibility and first-order shear deformation theory (FSDT), is utilized for computation of hydrostatic collapse pressure of the imperfect cross-ply ring. Numerical results pertaining to the effect of modal imperfection on the hydrostatic collapse pressure of a moderately thick cross-ply ring and comparison with its perfect counterpart are also presented. These results further demonstrate that the present iterative analysis for solving a nonlinear eigenvalue problem reduces to the linearized buckling (linear eigenvalue) analysis, associated with the conventional bifurcation theory, for a perfect moderately thick cross-ply ring.

This paper is concerned with a compact finite difference method for solving systems of two-dimensional reaction–diffusion equations. This method has the accuracy of fourth-order in both space and time. The existence and uniqueness of the finite difference solution are investigated by the method of upper and lower solutions, without any monotone requirement on the nonlinear term. Three monotone iterative algorithms

This article presents a novel method for acquiring high-quality solid models of complex 3D shapes from multiple calibrated photographs. After the purely geometric constraints associated with the silhouettes found in each image have been used to construct a coarse surface approximation in the form of a visual hull, photoconsistency constraints are enforced in three consecutive steps: (1) the rims where the surface grazes the visual hull are first identified through dynamic programming; (2) with the rims now fixed, the visual hull is carved using graph cuts to globally optimize the photoconsistency of the surface and recover its main features; (3) an iterative (local) refinement step is finally used to recover fine surface details. The proposed approach has been implemented, and experiments with seven real data sets are presented, along with qualitative and quantitative comparisons with several state-of-the-art image-based-modeling algorithms.

We describe a parallel iterative least squares solver named LSRN that is based on random normal projection. LSRN computes the min-length solution to min x∈R n Ax − b 2 , where A ∈ R m×n with m n or m n, and where A may be rank-deficient. Tikhonov regularization may also be included. Since A is only involved in matrix-matrix and matrix-vector multiplications, it can be a dense or sparse matrix or a linear operator, and LSRN automatically speeds up when A is sparse or a fast linear operator. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size γ min(m, n) × min(m, n), where γ is moderately larger than 1, e.g., γ = 2. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predictable when we apply LSQR or the Chebyshev semi-iterative method. As we demonstrate, the Chebyshev method is particularly efficient for solving large problems on clusters with high communication cost. Numerical results demonstrate that on a shared-memory machine, LSRN outperforms LAPACK's DGELSD on large dense problems, and MATLAB's backslash (SuiteSparseQR) on sparse problems. Further experiments demonstrate that LSRN scales well on an Amazon Elastic Compute Cloud cluster.

We present through the algorithmic language DHL (Dijkstra-Hehner language), a practical approach to a simple first order theory based on calculational logic, unifying Hoare and Dijkstra's iterative style of programming with Hehner's recursive predicative programming theory, getting the "best of the two worlds" and without having to recur in any way to higher-order approaches such as predicate transformers, Hoare logic, fixed-point or relational theory.

This paper presents a text word extraction algorithm that takes a set of bounding boxes of glyphs and their associated text lines of a given document and partitions the glyphs into a set of text words, using only the geometric information of the input glyphs. The algorithm is probability based. An iterative, relaxation-like method is used to find the partitioning solution that maximizes the joint probability. To evaluate the performance of our text word extraction algorithm, we used a 3-fold validation method and developed a quantitative performance measure. The algorithm was evaluated on the UW-III database of some 1600 scanned document image pages. An area-overlap measure was used to find the correspondence between the detected entities and the ground-truth.

Many intensive care units (ICUs) face overcrowding. One response to this overcrowding is to bump ICU patients to other departments of the hospital to make room for new patient arrivals. Such bumping clearly has the potential to reduce quality of care. In this paper we develop a stochastic model of a single ICU with patient bumping. The purpose of this model is to enable planners to predict performance, in terms of bumping, under differing arrival patterns and capacity. We develop a Markov chain model and a new aggregation-disaggregation algorithm for this problem that enables us to keep track of the time in system for each patient despite the high dimensionality of the problem. Our approach allows for more accurate modeling of the system than previous work that assumed an exponential distribution for length of stay (LOS). We also demonstrate the superior computational efficiency of our approach over the Gauss-Seidel iterative method for solving the Markov chain. Finally, we use the model to explore how different surgery schedules influence bumping rates.

A useful method of modeling viscoelastic effects in structures for transient response analysis is to treat the frequency dependence of the usual damping model through the introduction of extra dissipation coordinates or internal variables. These new coordinates require a curve t to the material loss factor data over a range of frequencies. Such a method has the disadvantage of introducing a large number of extra degrees of freedom that make response calculations and controller design very computationally intensive. Methods are examined to reduce the model size and, hence, ease this burden. Eigensystem truncation and balanced realizations are used to successfully reduce the full model. It is demonstrated that methods where the reduction transformation is based on the undamped model produce poor results. An iterative method to calculate the full eigensystem is introduced, using the frequency-dependent material modulus. In an alternative scheme, the model based on the physical degrees of freedom is reduced before the extra dissipation coordinates for the Golla-Hughes-McTavish method are introduced. Also considered is the possibility of reducing the model at the element level, before assembly, although this approach has dif culty retaining the damping characteristics of the full model.

A spatial-resolution reduction based framework for incorporation of a Wyner-Ziv frame coding mode in existing video codecs is presented, to enable a mode of operation with low encoding complexity. The core Wyner-Ziv frame coder works on the Laplacian residual of a lower-resolution frame encoded by a regular codec at reduced resolution. The quantized transform coefficients of the residual frame are mapped to cosets to reduce the bit-rate. A detailed ratedistortion analysis and procedure for obtaining the optimal parameters based on a realistic statistical model for the transform coefficients and the side information is also presented. The decoder iteratively conducts motion-based sideinformation generation and coset decoding, to gradually refine the estimate of the frame. Preliminary results are presented for application to the H.263+ video codec.

An efficient algorithm for the direct solution of a linear system associated with the discretization of boundary integral equations with oscillatory kernels (in two dimensions) is described without having to compute the complete matrix of the linear system. This algorithm is based on the unitary-weight representation, for which a new construction based on adaptive cross approximation is proposed. This low rank approximation uses only a small part of the entries to construct the adaptive cross representation, and therefor the linear system can be solved efficiently.

For an edge-weighted connected undirected graph, the minimum k-way cut problem is to find a subset of edges of minimum total weight whose removal separates the graph into k connected components. The problem is NP-hard when k is part of the input and W[1]-hard when k is taken as a parameter. A simple algorithm for approximating a minimum k-way cut

This article describes recent technical developments that have made the total-energy pseudopotential the most powerful {ital ab} {ital initio} quantum-mechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in

Linear mixed-effects models are an important class of statistical models that are not only used directly in many fields of applications but also used as iterative steps in fitting other types of mixed-effects models, such as generalized linear mixed models. The parameters in these models are typically estimated by maximum likelihood (ML) or restricted maximum likelihood (REML). In general there is no closed form solution for these estimates and they must be determined by iterative algorithms such as EM iterations or general nonlinear optimization. Many of the intermediate calculations for such iterations have been expressed as generalized least squares problems. We show that an alternative representation as a penalized least squares problem has many advantageous computational properties including the ability to evaluate explicitly a profiled log-likelihood or log-restricted likelihood, the gradient and Hessian of this profiled objective, and an ECME update to refine this objective.

This paper proposes a power saving control method for battery-powered portable wireless LAN (WLAN) access points (APs) in an overlapping basic service set (OBSS) environment. The IEEE802.11 standard does not support power saving control for APs. Some conventional power saving control methods for APs have been proposed that use the network allocation vector (NAV) to inhibit transmission at stations (STAs) while the AP is sleeping. However, since with these approaches the actual beacon interval in the OBSS environment may be extended due to the NAV as compared to the beacon interval which is set at the AP, the power consumption and delay may be increased as compared to a single BSS unaffected by interference from neighboring APs. To overcome this problem, this paper introduces a new action frame named power saving access point (PSAP) action frame which the AP uses to inform STAs within its BSS about the AP's sleep length. In addition, a function of the PSAP action frame is that STAs enter the sleep state after receiving the PSAP action frame. The proposed control method avoids the postponement of beacon transmission and reduces the power consumption in an OBSS environment, as compared to the conventional control method. Numerical analysis and computer simulation reveal that the newly proposed control method conserves power as compared to the conventional control method. The proposed control method achieves the minimum consumed power ratio at the AP, which is 44% as compared to the standard, when the beacon interval is 100 ms and the sleep length is 60 ms, even if the number of neighboring APs in an OBSS environment is increased.

The authors describe how to construct systematically a prefilter for the data entering the identifier, when the task of the latter is to provide a reduced-order plant model to be used for offsetfree LQG control with integral action. The problem of choosing suitable dynamic weights for the control performance index is also addressed via a complementary identification procedure acting on the residual errors.

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Règles positionnelles itératives, principe majoritaire et préférences unimodales RAIRO. Recherche opérationnelle, tome 34, n o 3 (2000), p. 347-362 <http://www.numdam.org/item?id=RO_2000__34_3_347_0> © AFCET, 2000, tous droits réservés. L'accès aux archives de la revue « RAIRO. Recherche opérationnelle » implique l'accord avec les conditions générales d'utilisation (http://www. numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ RAIRO Opérations Research RAIRO Oper. Res. 34 (2000) 347-362 RÈGLES POSmONNELLES ITÉRATIVES, PRINCIPE MAJORITAIRE ET PRÉFÉRENCES UNIMODALES (*) par Dominique LEPELLEY (*) et Laurent VIDU (*) Communiqué par Jean-Yves JAFFRÂY Resumé.-Les règles positionneUes itératives sont des règles de choix collectif procédant par éliminations successives et dans lesquelles le score des options est calculé sur la base des positions qu 'elles occupent dans les ordres de préférence des individus prenant part à la décision collective. Le présent article se propose d'étudier l'aptitude de ces règles à choisir l'option majoritaire (ou fortement majoritaire) lorsque les préférences des individus sont unimodales.

Self-twisting composite marine propellers, when subject to hydrodynamic loading, will not only automatically bend but also twist due to passive bend-twist (BT) coupling characteristics of anisotropic composites. To exploit the BT coupling effects of self-twisting propellers, a two-level (material and geometry) design methodology is proposed, formulated, and implemented. The material design is formulated as a constrained, discrete, binary optimization problem, which is tackled using an enhanced genetic algorithm equipped with numerical and analytical tools as function evaluators. The geometry design is formulated as an inverse problem to determine the unloaded geometry, which is solved using an over-relaxed, nonlinear, iterative procedure. A sample design is provided to illustrate the design methodology, and the predicted performance is compared to that of a rigid propeller. The results show that the selftwisting propeller produced the same performance as the rigid propeller at the design flow condition, and it produced better performance than the rigid propeller at off-design flow conditions, including behind a spatially varying wake.

The problem of learning from data involving function values and gradients is considered in a framework of least-square regularized regression in reproducing kernel Hilbert spaces. The algorithm is implemented by a linear system with the coefficient matrix involving both block matrices for generating Graph Laplacians and Hessians. The additional data for function gradients improve learning performance of the algorithm. Error analysis is done by means of sampling operators for sample error and integral operators in Sobolev spaces for approximation error.

Ordinal data are often modeled using a continuous latent response distribution, which is partially observed through windows of adjacent intervals de¯ned by cutpoints. In this paper we propose the beta distribution as a model for the latent response. The beta distribution has several advantages over the other common distributions used, e.g., normal and logistic. In particular, it enables separate modeling of location and dispersion e®ects which is essential in the Taguchi method of robust design. First, we study the problem of estimating the location and dispersion parameters of a single beta distribution (representing a single treatment) from ordinal data assuming known equispaced cutpoints. Two methods of estimation are compared: the maximum likelihood method and the method of moments. Two methods of treating the data are considered: in raw discrete form and in smoothed continuousized form. A large scale simulation study is carried out to compare the di®erent methods. The mean square errors of the estimates are obtained under a variety of parameter con¯gurations. Comparisons are made based on the ratios of the mean square errors (called the relative e±ciencies). No method is universally the best, but the maximum likelihood method using continuousized data is found to perform generally well, especially for estimating the dispersion parameter. This method is also computationally much faster than the other methods and does not experience convergence di±culties in case of sparse or empty cells. Next, the problem of estimating unknown cutpoints is addressed. Here the multiple treatments setup is considered since in an actual application, cutpoints are common to all treatments, and must be estimated from all the data. A two-step iterative algorithm is proposed for estimating the location and dispersion parameters of the treatments, and the cutpoints. The proposed beta model and McCullagh's (1980) proportional odds model are compared by¯tting them to two real data sets.

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamics applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. We illustrate these features on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately_ and they can be combined synergistically. We include sample performance results from an Intel iPSC/860 hypercube implementation.

Antennas for radiating high-power mesoband (medium-bandwidth) electromagnetic signals are critical to the mission of upsetting electronics at a distance. When operated at frequencies of a few hundred megahertz, RF weapons require highly efficient antennas that can fit into a small volume. Most of the existing antennas, such as pyramidal horns, are too large to fit onto certain platforms of interest. To address this challenge, we investigate the folded horn, which has aperture dimensions of 0.5 2 wavelengths, and a depth of 1.5-2 wavelengths. This antenna has a nearly focused aperture field, due to a parabolic fold in the H-plane. We report here on the fabrication and testing of the first folded horn, operating at 3 GHz. After a number of iterations, we obtained a realized gain of at least 10 dBi over 3-5 GHz, an aperture efficiency of 80%, and a return loss below 10 dB over 2.8-3.35 GHz. This design could be adapted to high voltages, and it could work well in a 2-antenna array, with two antennas positioned back-to-back, driven by a differential source.

This paper is concerned with estimating the solutions of numerically ill-posed least squares problems through Tikhonov regularization. Given a priori estimates on the covariance structure of errors in the measurement data b, and a suitable statistically-chosen σ, the Tikhonov regularized least squares functional J(σ) = Ax − b 2 W b + 1/σ 2 D(x − x 0) 2 2 , evaluated at its minimizer x(σ), approximately follows a χ 2 distribution withm degrees of freedom. Herem = m + p − n for A ∈ R m×n , D ∈ R p×n , matrix W b is the inverse covariance matrix of the mean 0 normally distributed measurement errors e in b, and x 0 is an estimate of the mean value of x. Using the generalized singular value decomposition of the matrix pair [W 1/2 b AD], σ can then be found such that the resulting J follows this χ 2 distribution, Mead and Renaut (2008). Because the algorithm explicitly relies on the direct solution of the problem obtained using the generalized singular value decomposition it is not practical for large scale problems. Here the approach is extended for large scale problems through the use of the Newton iteration in combination with a Golub-Kahan iterative bidiagonalization of the regularized problem. The algorithm is also extended for cases in which x 0 is not available, but instead a set of measurement data provides an estimate of the mean value of b. The sensitivity of the Newton algorithm to the number of steps used in the Golub-Kahan iterative bidiagonalization, and the relation between the size of the projected subproblem and σ are discussed. Experiments presented contrast the efficiency and robustness with other standard methods for finding the regularization parameter for a set of test problems and for the restoration of a relatively large real seismic signal. An application for image deblurring also validates the approach for large scale problems. We conclude that the presented approach is robust for both small and large scale discretely ill-posed least squares problems.