Jacobi Algorithm

Este  artículo  describe  una  situación  en  donde  se tiene una reacción de isomerización de un compuesto A dentro de un reactor tipo Tanque Agitado Continuo en estado estacionario.Los métodos utilizados para obtener las concentraciones de salida de un reactor tipo tanque agitado continuo en estado estacionario, son  los  métodos  iterativos  de  Jacobi  y  Gauss-Seidel.  Dichos métodos consisten en recalcular las soluciones de las variables xi a partir de un valor inicial estimado, usando las ecuaciones dadas teniendo  como  base  una  tolerancia  de  0.05  en  las  mediciones realizadas.  Los  resultados  para  las  concentraciones  del  proceso se  obtuvieron  luego  de  4  iteraciones  con  el  método  de  Jacobi,  y 1  iteración  con  el  método  de  Gauss-Seidel.

In this paper, we apply the Jacobi iterative algorithm to combat intersymbol interference (ISI) caused by frequency selective channels. The performance bound of the equalizer is analyzed in order to gain an insight into its asymptotic behavior. Due to the error propagation problem, the potential of this algorithm is not reached in an uncoded system. However, its extension to a coded system with the application of the turbo processing principle results in a new turbo equalization algorithm which demonstrates comparable performance with reduced complexity compared to some existing filter based turbo equalization schemes; and superior performance compared to some frequency domain solutions, such as orthogonal frequency division multiplexing (OFDM) and single-carrier frequency domain equalization (SC-FDE). * This work has been presented in part at the IEEE International Conference on Communications (ICC) 2008.

This paper proposes a novel optimized model based on the combination of the fuzzy time series (FTS) method and Jacobi polynomials for predicting the behavior of fiber‐reinforced polymer (FRP)‐confined concrete under compression loads. In this model, the stress‐strain curves are approximated by Jacobi polynomials. Then, the FTS method is used to develop a nonlinear relationship between the coefficients of Jacobi polynomials and the specimen features. Moreover, another FTS model is developed to predict the ultimate stress and the ultimate strain of FRP‐confined concrete. A comparative analysis is performed to demonstrate the effectiveness of the proposed model. As compared with the well‐known design‐oriented models applied to 69 experiments, the root mean square error is decreased more than 50% by the proposed model. Also, the effects of input features on the physical behavior of the specimens as described by the proposed model are consistent with the relevant theories and experiments.

The paper investigates a distributed control system scheme for urban road traffic management. The control algorithm is based on model predictive control (MPC) involving Jacobi iteration algorithm to solve constrained and nonlinear programming problem.
The signal controllers of traffic network constitute a network of computers. They can distribute their computation realizing an efficient traffic control without any central management. However the optimal control inputs can be also calculated by a single traffic controller if the traffic network contains few intersections.
The control aim is to relieve traffic congestion, reduce travel time and improve homogenous traffic flow in urban traffic area using distributed control architecture. The MPC based control strategy can be implemented in any urban transportation network but adequate measurement system and modern traffic controllers are needed. Theory, realization possibilities and simulation of the control method are also presented. The simulation results show that the system is able to ameliorate the network efficiency and reduce travel time. The distributed MPC based traffic control strategy proves the effectiveness by realizing a dependable control operation and creating optimal flow in the network subjected to control input constraints.

The shared-memory model has been adopted, both for data exchange as well as synchronization using semaphores in almost every on-chip multiprocessor implementation, ranging from general purpose chip multiprocessors (CMPs) to domain specific multi-core graphics processing units (GPUs). Low-latency synchronization is desirable but is hard to achieve in practice due to the memory hierarchy. On the contrary, an explicit exchange of synchronization tokens among the processing elements through dedicated on-chip links would be beneficial for the overall system performance. In this paper we propose the Medea NoC-based framework, a hybrid shared-memory/message-passing approach. Medea has been modeled with a fast, cycle-accurate SystemC implementation enabling a fast system exploration varying several parameters like number and types of cores, cache size and policy and NoC features. In addition, every SystemC block has its RTL counterpart for physical implementation on FPGAs and ASICs. A parallel version of the Jacobi algorithm has been used as a test application to validate the metodology. Results confirm expectations about performance and effectiveness of system exploration and design.

An intimate connection between matrix eigenvMue algorithms and integrable dynamical systems is studied. It is proved that an infinitesimal rotation of each step of the Jacobi algorithm for symmetric eigenwlue problem is an integrable gradient system of Lax form.

Systems of linear equations appear in many areas either directly as in modeling physical situations or indirectly as in the numerical solutions of other mathematical models. The solution of the linear equations' system is probably the most important issue in numerical methods like the finite element method (FEM). Using the finite element method in modeling various structures, with either simple or complicated configuration of elements, in structural engineering became prevalent many years ago. There are two main types of solvers depending on whether the used method is direct or iterative (indirect) method. In contrast to the iterative techniques, the direct techniques provide almost exact solutions, however they are not convenient for some situations, including but not limited to huge systems of equations. In such situations, the iterative solvers are favored as they have privileges concerning solving speed and storage requirements. In addition, indirect solvers are simpler to program. This research focuses on using the Classical (Stationary) iterative techniques for solving linear systems of equations. The main objective of this research is to develop a new modified version of the well-known Gauss-Seidel (GS) iterative technique which is adapted to solving problems in structural engineering. The proposed technique remarkably outperforms GS technique regarding the required number of iterations and the convergence speed. In this paper, the differences between the direct and iterative approaches have been discussed, along with a quick overview of some of the methods underlying these two classes. Then, the idea and algorithm of the new proposed-Modified Gauss-Seidel‖ (MGS) technique have been elucidated. Afterward, the algorithm has been programmed and used to solve some 2D Practical Examples, besides using the conventional Jacobi and GS techniques. Finally, the obtained results have been compared to assess the proposed MGS; it outperformed both Jacobi and GS.

The objective of this research is to construct parallel implementations of the Jacobi algorithm used for the solution of linear algebraic systems, to measure their speedup with respect to the serial case and to compare each other, regarding their efficiency. The programming paradigm used in this implementation is the message passing model, while, the MPI implementation used is the MPICH implementation of the Argonne National Laboratory.

The paper investigates a distributed control system scheme for urban road traffic management. The control algorithm is based on model predictive control (MPC) involving Jacobi iteration algorithm to solve constrained and nonlinear programming problem. The signal controllers of traffic network constitute a network of computers. They can distribute their computation realizing an efficient traffic control without any central management. However the optimal control inputs can be also calculated by a single traffic controller if the traffic network contains few intersections. The control aim is to relieve traffic congestion, reduce travel time and improve homogenous traffic flow in urban traffic area using distributed control architecture. The MPC based control strategy can be implemented in any urban transportation network but adequate measurement system and modern traffic controllers are needed. Theory, realization possibilities and simulation of the control method are also presented. The simulation results show that the system is able to ameliorate the network efficiency and reduce travel time. The distributed MPC based traffic control strategy proves the effectiveness by realizing a dependable control operation and creating optimal flow in the network subjected to control input constraints. Keywords urban traffic control • model predictive control • distributed traffic control system • Jacobi algorithm

Pada abad 21 ini, dimana segala macam alat-alat teknologi harus berukuran lebih kecil, Micro Electro Mechanical Systems atau MEMS sudah banyakdigunakan pada berbagai macam bidang teknologi. MEMS sendiri adalahsebuah miniatur perangkat atau susunan perangkat berukuran mikro yang menggabungkan komponen elektrik dan mekanik. Pada masa mendatang, di prediksi akan terdapat teknologi yang dapat mengintegrasikan MEMS keda- lam sebuah projectile. Ada beragam manfaat pengintegrasian MEMS pada proyektil, contohnya adalah pemasangan GPS pada proyektil ataupun untuk meningkatkan akurasi penembakan karena dengan pemasangan MEMS pada proyektil jalur penembakan proyektil dapat disesuaikan. Tetapi terdapat suatu masalah ketika mengintegrasikan MEMS kedalam sebuah projectile, yaitu MEMS hanya dapat bertahan sampai suhu 71 derajat Celcius atau 344 derajat
Kelvin, sedangkan suhu pada proyektil ketika ditembakan bisa mencapai 267 derajat Celcius atau 540 derajat Kelvin. Oleh karena itu maka akan cukup sulit untuk mengintegrasikan MEMS kedalam sebuah proyektil. Untuk mengatasi masalah tersebut, maka perlu dilakukan pemodelan untuk menentukan lokasi terbaik untuk meletakan MEMS pada proyektil menggunakan metode Jacobi. Dengan metode Jacobi suhu bagian dalam proyektil dapat dicari melalui proses iterasi yang menggunakan data suhu bagian permukaan proyektil.