Papers by Drahoslava Janovska
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics, 2011
Qualitative methods for continuous dynamical systems are used to analyze local and global propert... more Qualitative methods for continuous dynamical systems are used to analyze local and global properties of Filip‐pov systems. The phase portrait, stability and bifurcations are investigated by potential, pseudopotential, Hamiltonian and pseudohamiltonian of the given system.
ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010, 2010
The Filippov systems theory is applied to selected problems from biology and chemical engineering... more The Filippov systems theory is applied to selected problems from biology and chemical engineering, namely we explore and simulate Bazykin’s ecological model, an ideal closed gas‐liquid system including its dimensionless formulation. The last investigated system is a CSTR with an outfall and the CSTR with a reactor volume control.
Applications of Mathematics, Dec 1, 1999
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz
River Publishers eBooks, Sep 1, 2022
Applications of Mathematics, 1984
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.
World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, Nov 20, 2008
A proof of convergence of a new continuation algorithm for computing the Analytic SVD for a large... more A proof of convergence of a new continuation algorithm for computing the Analytic SVD for a large sparse parameterdependent matrix is given. The algorithm itself was developed and numerically tested in [5].
Mathematics and Computers in Simulation, Jun 1, 2012
ABSTRACT The aim is to contribute to pseudospectra computation via a path following technique. Gi... more ABSTRACT The aim is to contribute to pseudospectra computation via a path following technique. Given a matrix A is an element of C-n x n, we compute the branch consisting of a fixed singular value c and corresponding left and right singular vectors of the parameter dependent matrix (x+ i gamma)I - A. The fact that the branch corresponds to the smallest singular value sigma(min)((x+i gamma)I - A) = is an element of is sufficient to verify at just one point of the branch due to the continuity argument. We can exploit a standard ready-made software. (c) 2012 IMACS. Published by Elsevier By. All rights reserved.
Applications of Mathematics, Feb 1, 2003
Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digi... more Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz 48 (2003) APPLICATIONS OF MATHEMATICS No. 1, 3-30
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008, 2008
ABSTRACT Given a matrix A ∊ n×n, we compute the branch consisting of a fixed singular value ε and... more ABSTRACT Given a matrix A ∊ n×n, we compute the branch consisting of a fixed singular value ε and corresponding left and right singular vectors of parameter dependent matrix (x+iy)I−A. The fact that the branch corresponds to the smallest singular value σmin((x+iy)I−A) = ε is sufficient to verify at just one point of the branch due to continuity argument. We can exploit standard ready‐made software.
Nucleation and Atmospheric Aerosols, 2007
In [1], we considered branches of selected singular values and the relevant left/right singular v... more In [1], we considered branches of selected singular values and the relevant left/right singular vectors. The nongeneric points related to nonsimple nonzero singular values on the path were treated as classical singularities of a mapping. The present contribution is devoted to the much complicated case of zero singular values, both simple and nonsimple, and corresponding left/right singular vectors. We will investigate genericity of the branching scenario.
Springer eBooks, Oct 7, 2007
ABSTRACT The aim is to compute ASVD for large sparse matrices. In particular we will consider bra... more ABSTRACT The aim is to compute ASVD for large sparse matrices. In particular we will consider branches of selected singular values and the corresponding left/right singular vectors. We apply a predictor-corrector algorithm with an adaptive stepsize control.
11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013, 2013
ABSTRACT We consider quaternionic polynomials in the most general form. More precisely, polynomia... more ABSTRACT We consider quaternionic polynomials in the most general form. More precisely, polynomials are arbitrary, finite, sums of monomials, where monomials of degree j have the form a0.x.a1.x.a2.x...x.aj-1.x.aj, with a variable j. This allows also several monomials of the same degree. Our aim is to apply Newton's method to compute zero points of these polynomials, namely to calculate the Jacobi matrix needed in Newton's method.
Advances in Applied Clifford Algebras, Dec 24, 2010
The field of quaternions, denoted by $${\mathbb{H}}$$ can be represented as an isomorphic four di... more The field of quaternions, denoted by $${\mathbb{H}}$$ can be represented as an isomorphic four dimensional subspace of $${\mathbb{R}^{4\times 4}}$$, the space of real matrices with four rows and columns. In addition to the quaternions there is another four dimensional subspace in $${\mathbb{R}^{4\times 4}}$$ which is also a field and which has – in connection with the quaternions – many pleasant properties. This field is called field of pseudoquaternions. It exists in $${\mathbb{R}^{4\times 4}}$$ but not in $${\mathbb{H}}$$. It allows to write the quaternionic linear term axb in matrix form as Mx where x is the same as the quaternion x only written as a column vector in $${\mathbb{R}^4}$$. And M is the product of the matrix associated with the quaternion a with the matrix associated with the pseudoquaternion b. Now, the field of quaternions can also be represented as an isomorphic four dimensional subspace of $${\mathbb{C}^{2\times 2}}$$ over $${\mathbb{R}}$$, the space of complex matrices with two rows and columns. We show that in this space pseudoquaternions with all the properties known from $${\mathbb{R}^{4\times 4}}$$ do not exist. However, there is a subset of $${\mathbb{C}^{2\times 2}}$$ for which some of the properties are still valid. By means of the Kronecker product we show that there is a matrix in $${\mathbb{C}^{4\times 4}}$$ which has the properties of the pseudoquaternionic matrix.
The number of real operations necessary to reduce a quaternion-valued matrix into a similar upper... more The number of real operations necessary to reduce a quaternion-valued matrix into a similar upper Hessenberg matrix by making use of quaternion-valued Givens’ transformation matrices is relatively large. Two possibilities of how to reduce the columns of a quaternion-valued matrix more effectively are presented.
Advances in Applied Clifford Algebras, Jul 24, 2018
We prove that the quaternionic companion polynomial is identical with the characteristic polynomi... more We prove that the quaternionic companion polynomial is identical with the characteristic polynomial of the complex matrix which is obtained by isomorphism from the quaternionic companion matrix. And we show that this is also true for the other three noncommutative algebras in R 4 which include the coquaternions.
Advances in Applied Clifford Algebras, Nov 11, 2015
We are concerned with matrices over nondivision algebras and show by an example from an R 4 algeb... more We are concerned with matrices over nondivision algebras and show by an example from an R 4 algebra that these matrices do not necessarily have eigenvalues, even if these matrices are invertible. The standard condition for eigenvectors x = 0 will be replaced by the condition that x contains at least one invertible component which is the same as x = 0 for division algebras. The topic is of principal interest, and leads to the question what qualifies a matrix over a nondivision algebra to have eigenvalues. And connected with this problem is the question, whether these matrices are diagonalizable or triangulizable and allow a Schur decomposition. There is a last section where the question whether a specific matrix A has eigenvalues is extended to all eight R 4 algebras by applying numerical means. As a curiosity we found that the considered matrix A over the algebra of tessarines, which is a commutative algebra, introduced by Cockle (Phil Mag 35(3):434-437, 1849; http:// www.oocities.org/cocklebio/), possesses eigenvalues.
AIP Conference Proceedings, 2009
We will study quadratic one sided quaternionic polynomials and their zeros. We apply the general ... more We will study quadratic one sided quaternionic polynomials and their zeros. We apply the general theory to this particular case, i.e. we divide the zeros into two classes: spherical and isolated zeros. By making use of the theory of companion polynomials we give an algorithm for computing all zeros of these polynomials.
Applications of Mathematics, Aug 10, 2023
Advances in Applied Clifford Algebras, Sep 27, 2013
We will present the general solution of the algebraic Riccati equation for the quaternionic case,... more We will present the general solution of the algebraic Riccati equation for the quaternionic case, where also one additional variation is treated. For computational purpose a very simple form of the exact Jacobi matrix for Riccati polynomials is presented. There are several examples.
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Papers by Drahoslava Janovska