Search Results - "Matrices over function rings in one or more variables"

On regular polynomial matrices. II. The associated matrix pencils; simple matrix pencils: On regular polynomial matrices. II: The associated matrix pencils; simple matrix pencils

Authors: Lee, Anna

Source: Publicationes Mathematicae Debrecen. 23:327-333

Subject Terms: Matrices over function rings in one or more variables, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/3574046

Matrix orthogonal polynomials associated with perturbations of block Toeplitz matrices

Authors: L. E. Garza Gaona A. E. Choque-Rivero

Source: Russian Mathematics. 61:57-69

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Toeplitz, Cauchy, and related matrices, Matrices over function rings in one or more variables, Toeplitz matrices, moment problem, unit circle, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, matrix orthogonal polynomials, 01 natural sciences

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Access URL: https://zbmath.org/6845964
https://doi.org/10.3103/s1066369x17120076
https://link.springer.com/article/10.3103/S1066369X17120076

To solving multiparameter problems of algebra. 6. Spectral characteristics of polynomial matrices: To solving multiparameter problems of algebra. 6: Spectral characteristics of polynomial matrices

Authors: V. N. Kublanovskaya

Source: Journal of Mathematical Sciences. 137:4835-4843

Subject Terms: Eigenvalues, singular values, and eigenvectors, spectral pairs, Matrices over function rings in one or more variables, Other matrix algorithms, 0101 mathematics, polynomial matrix, 01 natural sciences, spectrum

File Description: application/xml

Access URL: https://zbmath.org/2214028
https://www.infona.pl/resource/bwmeta1.element.springer-f7c3cba2-c563-365b-b85a-3df7f9ecd696
https://link.springer.com/article/10.1007/s10958-006-0281-9
https://eudml.org/doc/229281

The resultant approach to computing vector characteristics of multiparameter polynomial matrices: A resultant approach to computing vector characteristics of multiparameter polynomial matrices

Authors: V. B. Khazanov

Source: Journal of Mathematical Sciences. 137:4862-4878

Subject Terms: null space, Matrices over function rings in one or more variables, range, Other matrix algorithms, Sylvester matrix, multiparameter matrix polynomial, 0101 mathematics, Jordan chain, 01 natural sciences

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Access URL: https://zbmath.org/2214031
https://link.springer.com/article/10.1007/s10958-006-0284-6
https://eudml.org/doc/225607

On Some Spectral Characteristics of Multiparameter Polynomial Matrices: On some spectral characteristics of multiparameter polynomial matrices

Authors: V. B. Khazanov

Source: Journal of Mathematical Sciences. 132:236-239

Subject Terms: Eigenvalues, singular values, and eigenvectors, Matrices over function rings in one or more variables, eigenvectors, matrix solvents, spectral characteristics, polynomial matrices, 0101 mathematics, 01 natural sciences, block eigenvalues, spectrum

File Description: application/xml

Access URL: https://zbmath.org/2213793
https://link.springer.com/10.1007%2Fs10958-005-0492-5
https://link.springer.com/article/10.1007/s10958-005-0492-5

Spectral factorization of non-symmetric polynomial matrices

Authors: Jovan Stefanovski

Source: Linear Algebra and its Applications. 412:412-440

Subject Terms: Polynomial spectral factorization, 0209 industrial biotechnology, Eigenvalues, singular values, and eigenvectors, inner-outer factorization, 02 engineering and technology, Invariant subspace, integer linear programming, Deflating subspace, invariant subspace, 0203 mechanical engineering, Matrices over function rings in one or more variables, greatest common divisor, Matrix pencil, matrix pencil, Discrete Mathematics and Combinatorics, polynomial matrix, Numerical Analysis, Algebra and Number Theory, eigenvalues, polynomial spectral factorization, Matrices, determinants in number theory, deflating subspace, Polynomial matrix, Multiplicative structure, Euclidean algorithm, greatest common divisors, Geometry and Topology, Matrix pencils

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Access URL: https://core.ac.uk/display/82583143
https://www.sciencedirect.com/science/article/abs/pii/S0024379505003599

Efficient algorithms for the matrix cosine and sine

Authors: Hargreaves, Gareth I. Higham, Nicholas J.

Source: Hargreaves, G I & Higham, N J 2005, 'Efficient algorithms for the matrix cosine and sine', Numerical Algorithms, vol. 40, no. 4, pp. 383-400. https://doi.org/10.1007/s11075-005-8141-0

Subject Terms: MATLAB, Double-angle formula, Matrix function, Schur-Parlett method, Matrix sine, 01 natural sciences, matrix exponential, Padé approximant, Matrices over function rings in one or more variables, matrix function, Taylor series, matrix cosine, Matrix cosine, double-angle formula, 0101 mathematics, Padé approximation, numerical examples, algorithm, 4. Education, Other matrix algorithms, Matrix equations and identities, error bounds, Matrix exponential, rounding error analysis, Rounding error analysis, Computation of special functions and constants, construction of tables, matrix sine

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Access URL: http://eprints.maths.manchester.ac.uk/124/1/paper2.pdf

Linear dependence of quotients of analytic functions of several variables with the least subcollection of generalized Wronskians

Authors: Ronald A. Walker

Source: Linear Algebra and its Applications. 408:151-160

Subject Terms: Numerical Analysis, Vector spaces, linear dependence, rank, lineability, Algebra and Number Theory, Higher-dimensional partitions, higher-dimensional partitions, 01 natural sciences, Young-like sets, linear dependence, Generalized Wronskians, Matrices over function rings in one or more variables, analytic functions of several variables, Linear dependence, Analytic functions of several variables, Meromorphic functions of several complex variables, Discrete Mathematics and Combinatorics, generalized wronskians, Geometry and Topology, 0101 mathematics

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Access URL: https://zbmath.org/2213087
https://doi.org/10.1016/j.laa.2005.06.002
https://core.ac.uk/display/82658814
https://pennstate.pure.elsevier.com/en/publications/linear-dependence-of-quotients-of-analytic-functions-of-several-v
https://www.sciencedirect.com/science/article/pii/S0024379505002685

Bezoutians, Euclidean Algorithm, and Orthogonal Polynomials: Bezoutians, Euclidean algorithm, and orthogonal polynomials

Authors: Alain Lascoux Piotr Pragacz

Source: Annals of Combinatorics. 9:301-319

Subject Terms: Real and complex fields, Symmetric functions and generalizations, Matrices over function rings in one or more variables, Lagrange interpolation, continued fractions, Other special orthogonal polynomials and functions, 0102 computer and information sciences, 0101 mathematics, Orthogonal polynomials (combinatorics), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 01 natural sciences, Schur functions

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Access URL: https://www.impan.pl/~pragacz/download/bez7.pdf
https://www.infona.pl/resource/bwmeta1.element.springer-e195ac2e-32e1-3185-8166-2af25e6a6842
https://link.springer.com/article/10.1007%2Fs00026-005-0259-1

Functions of matrices

Authors: Luis Verde-Star

Source: Linear Algebra and its Applications. 406:285-300

Subject Terms: Numerical Analysis, Hadamard product, Algebra and Number Theory, Dynamic solutions, Functions of a matrix, Horner polynomials, functions of matrices, resolvent, Matrix exponential, 01 natural sciences, Matrices over function rings in one or more variables, Cayley-Hamilton theorem, Cayley–Hamilton, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics, power series

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Access URL: https://zbmath.org/2210324
https://doi.org/10.1016/j.laa.2005.04.016
http://www.sciencedirect.com/science/article/pii/S0024379505002405
https://www.sciencedirect.com/science/article/pii/S0024379505002405

Numerical computation of minimal polynomial bases: A generalized resultant approach: Numerical computation of minimal polynomial bases: a generalized resultant approach

Authors: Stavros Vologiannidis Antonis I. G. Vardulakis Efstathios N. Antoniou

Source: Linear Algebra and its Applications. 405:264-278

Subject Terms: Numerical Analysis, 0209 industrial biotechnology, algorithm, Algebra and Number Theory, Canonical forms, reductions, classification, resultant based method, Other matrix algorithms, Matrix fraction description, 02 engineering and technology, Sylvester resultants, 01 natural sciences, Minimal polynomial basis, Matrices over function rings in one or more variables, Polynomial matrices, matrix fraction description, Discrete Mathematics and Combinatorics, minimal polynomial basis, Geometry and Topology, 0101 mathematics, polynomial matrix

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Access URL: https://zbmath.org/2189262
https://doi.org/10.1016/j.laa.2005.03.017
https://core.ac.uk/display/82223853
https://www.sciencedirect.com/science/article/pii/S0024379505001849
http://anadrasis.web.auth.gr/svol/papers/LAA05.pdf

Matrices that preserve the value of the generalized matrix function of the upper triangular matrices

Authors: Rosário Fernandes

Source: Linear Algebra and its Applications. 401:47-65

Subject Terms: Yang diagram, Numerical Analysis, generalized matrix function, Algebra and Number Theory, matrix preservers, permutation matrix, generalized Schur function, Generalized matrix function, Linear transformations, semilinear transformations, Matrix preservers, Determinants, permanents, traces, other special matrix functions, 01 natural sciences, Matrices over function rings in one or more variables, triangular matrix, Triangular matrix, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics

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Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0024379503007183
https://core.ac.uk/display/82186221

Solution of spectral problems for polynomial matrices

Authors: V. N. Kublanovskaya

Source: Journal of Mathematical Sciences. 127:2024-2032

Subject Terms: Eigenvalues, singular values, and eigenvectors, Matrices over function rings in one or more variables, greatest common divisor, Other matrix algorithms, Numerical solutions to inverse eigenvalue problems, inverse eigenvalue problem, polynomial matrices, 02 engineering and technology, 0101 mathematics, Inverse problems in linear algebra, 0210 nano-technology, 01 natural sciences, factorizations

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Access URL: https://zbmath.org/2214096
https://doi.org/10.1007/s10958-005-0160-9
https://link.springer.com/article/10.1007/s10958-005-0160-9

Linear preservers of zeros of matrix polynomials

Authors: Alexander Guterman Seok-Zun Song Sang-Gu Lee et al.

Source: Linear Algebra and its Applications. 401:325-340

Subject Terms: Numerical Analysis, Algebra and Number Theory, Matrices over special rings (quaternions, finite fields, etc.), Linear transformations, semilinear transformations, Matrix equations and identities, Semirings, linear transformation, 01 natural sciences, commutators, Matrix polynomials, Matrices over function rings in one or more variables, Discrete Mathematics and Combinatorics, Linear preservers, Geometry and Topology, 0101 mathematics, linear preservers, semirings, matrix polynomials

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Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0024379504003520
https://core.ac.uk/display/81943159
https://www.sciencedirect.com/science/article/pii/S0024379504003520

Displacement structures and fast inversion formulas for confluent polynomial Vandermonde-like matrices

Authors: Yong-Jian Hu Zheng-Hong Yang LaiSheng Wang

Source: Journal of Computational and Applied Mathematics. 177:1-15

Subject Terms: displacement structure, Applied Mathematics, Displacement structure, confluent Cauchy-like matrices, multiple interpolation nodes, 01 natural sciences, matrix inversion, Computational Mathematics, polynomial Cauchy-like matrices, Polynomial Vandermonde-like matrix, Matrices over function rings in one or more variables, inversion formula, Inversion formula, Hermitian, skew-Hermitian, and related matrices, Theory of matrix inversion and generalized inverses, 0101 mathematics, Interpolation in approximation theory, polynomial Vandermonde-like matrix

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Access URL: https://core.ac.uk/display/82007468
http://ui.adsabs.harvard.edu/abs/2005JCoAM.180..229Y/abstract
https://www.sciencedirect.com/science/article/abs/pii/S0377042704003590
https://www.sciencedirect.com/science/article/pii/S0377042704003590

Methods for solving spectral problems for multiparameter matrix pencils

Authors: V. B. Khazanov

Source: Journal of Mathematical Sciences. 127:2033-2050

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, eigenvector, Eigenvalues, singular values, and eigenvectors, complex matrices, Matrices over function rings in one or more variables, Newton method, partial eigenproblem, multiparameter regular pencils, polynomial matrices, 0101 mathematics, Matrix pencils, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2214097
https://doi.org/10.1007/s10958-005-0161-8
https://link.springer.com/article/10.1007/s10958-005-0161-8
https://link.springer.com/10.1007/s10958-005-0161-8

On the Pseudospectra of Matrix Polynomials: On the pseudospectra of matrix polynomials

Authors: Peter Lancaster Panayiotis Psarrakos

Source: SIAM Journal on Matrix Analysis and Applications. 27:115-129

Subject Terms: Numerical computation of eigenvalues and eigenvectors of matrices, Eigenvalues, singular values, and eigenvectors, perturbation, Numerical computation of matrix norms, conditioning, scaling, singular value, vibrating system, stability, 01 natural sciences, wing problem, boundary, gyroscopic system, Matrices over function rings in one or more variables, \(\varepsilon\)-pseudospectrum, eigenvalue, curve-tracing algorithm, 0101 mathematics, prediction-correction continuation, numerical experiments, matrix polynomial

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Access URL: https://zbmath.org/2206332
https://doi.org/10.1137/s0895479804441420

A primer of Perron–Frobenius theory for matrix polynomials: A primer of Perron--Frobenius theory for matrix polynomials

Authors: Michael J. Tsatsomeros Panayiotis Psarrakos

Source: Linear Algebra and its Applications. 393:333-351

Subject Terms: Perron–Frobenius, spectral radius, Nonnegative matrix, Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, numerical range, companion matrix linearization, nonnegative matrix, 01 natural sciences, Perron-Frobenius theory, spectrum, Positive matrices and their generalizations, cones of matrices, Matrix polynomial, Matrices over function rings in one or more variables, Discrete Mathematics and Combinatorics, multistep difference equation, Geometry and Topology, Numerical range, 0101 mathematics, Spectral radius, Multistep difference equation, matrix polynomial, Perron polynomial

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Access URL: https://zbmath.org/2126359
https://doi.org/10.1016/j.laa.2003.12.026
http://www.sci.wsu.edu/math/faculty/tsat/files/pfp.pdf
https://core.ac.uk/display/38441490
https://www.sciencedirect.com/science/article/pii/S002437950300898X
http://www.math.wsu.edu/math/faculty/tsat/files/pfp.pdf

On the exponentials of some structured matrices

Authors: Viswanath Ramakrishna F. Costa

Source: Journal of Physics A: Mathematical and General. 37:11613-11627

Subject Terms: quaternions, Lie groups, Lie algebra, FOS: Physical sciences, structured matrices, Mathematical Physics (math-ph), skew-symmetric matrices, symmetric Toeplitz matrices, algorithms, 01 natural sciences, Clifford algebras, matrix exponential, skew-Hamiltonian matrices, Matrices over function rings in one or more variables, 0103 physical sciences, per skew symmetric matrices, 0101 mathematics, normal matrices, Mathematical Physics

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Access URL: http://arxiv.org/pdf/math-ph/0407042
http://arxiv.org/abs/math-ph/0407042
https://arxiv.org/abs/math-ph/0407042
https://iopscience.iop.org/article/10.1088/0305-4470/37/48/007
http://core.ac.uk/display/2556058
https://ui.adsabs.harvard.edu/abs/2004JPhA...3711613R/abstract
https://www.arxiv-vanity.com/papers/math-ph/0407042/

A vector-bundle version of a theoremof V. Doležal: A vector-bundle version of a theorem of V. Doležal

Authors: Kevin A. Grasse

Source: Linear Algebra and its Applications. 392:45-59

Subject Terms: Numerical Analysis, topological space, Algebra and Number Theory, Vector bundles, Doležal's theorem, 01 natural sciences, Matrices over function rings in one or more variables, Contractible spaces, kernel, range, matrix function, Matrices depending on a parameter, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics, Block singular value decomposition, differentiable manifold

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Access URL: https://www.sciencedirect.com/science/article/pii/S0024379504002629
https://core.ac.uk/display/82384396