Nonlinearizing two-parameter eigenvalue problems

Συγγραφείς: Ringh, Emil, Author, Jarlebring, Elias, Author

Συνεισφορές: Ringh, Emil, Author, Jarlebring, Elias, Author

Πηγή: SIAM Journal on Matrix Analysis and Applications. 42(2):775-799

Θεματικοί όροι: two-parameter eigenvalue problem, nonlinear eigenvalue problem, multiparameter eigenvalue problem, iterative algorithms, implicit function theorem, Numerical Analysis, Numerisk analys, Tillämpad matematik och beräkningsmatematik, Applied and Computational Mathematics

Περιγραφή αρχείου: print

Σύνδεσμος πρόσβασης: https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291995
https://doi.org/10.1137/19M1274316

A new algorithm using L-BFGS for two-parameter eigenvalue problems from Lamé's system and simulation

Συγγραφείς: Hayati Ünsal Özer, Ahmet Duran

Πηγή: Mathematical Modelling and Numerical Simulation with Applications. 4:448-468

Σύνδεσμος πρόσβασης: https://avesis.yildiz.edu.tr/publication/details/490844b0-4b6a-4f65-b650-1a92b91b4d4e/oai

A modified two-parameter scaled Broyden-type algorithm for unconstrained optimization problems

Συγγραφείς: Yuan, Gonglin ^⁎, Wang, Zhan, Li, Pengyuan

Πηγή: In Journal of Computational and Applied Mathematics 1 October 2024 448

On the Two-parameter Matrix pencil Problem

Additional Titles: The multiparameter matrix pencil problem (MPP) is a generalization of the one-parameter MPP: given a set of $m\times n$ complex matrices $A_0,\ldots, A_r$, with $m\ge n+r-1$, it is required to find all complex scalars $λ_0,\ldots,λ_r$, not all zero, such that the matrix pencil $A(λ)=\sum_{i=0}^rλ_iA_i$ loses column rank and the corresponding nonzero complex vector $x$ such that $A(λ)x=0$. This problem is related to the well-known multiparameter eigenvalue problem except that there is only one pencil and, crucially, the matrices are not necessarily square. In this paper, we give a full solution to the two-parameter MPP. Firstly, an inflation process is implemented to show that the two-parameter MPP is equivalent to a set of three $m^2\times n^2$ simultaneous one-parameter MPPs. These problems are given in terms of Kronecker commutator operators (involving the original matrices) which exhibit several symmetries. These symmetries are analysed and are then used to deflate the dimensions of the one-parameter MPPs to $\frac{m(m-1)}{2}\times\frac{n(n+1)}{2}$ thus simplifying their numerical solution. In the case that $m=n+1$ it is shown that the two-parameter MPP has at least one solution and generically $\frac{n(n+1)}{2}$ solutions and furthermore that, under a rank assumption, the Kronecker determinant operators satisfy a commutativity property. This is then used to show that the two-parameter MPP is equivalent to a set of three simultaneous eigenvalue problems. A general solution algorithm is presented and numerical examples are given to outline the procedure of the proposed algorithm.

Συγγραφείς: Gungah, S. K., Alsubaie, F. F., Jaimoukha, I. M.

Όροι ευρετηρίου: Numerical Analysis, 15A22, 47A56, 47A80, 47A25, 15A69, 65F15, 15A18, 47B47, text

Σύνδεσμος: http://arxiv.org/abs/2406.17879

On the Two-Parameter Matrix Pencil Problem: On the two-parameter matrix pencil problem

Συγγραφείς: Satin K. Gungah, Fawwaz F. Alsubaie, Imad M. Jaimoukha

Πηγή: SIAM Journal on Matrix Analysis and Applications. 45:1287-1309

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, Eigenvalues, singular values, and eigenvectors, Kronecker product, Canonical forms, reductions, classification, multiparameter eigenvalue problem, Tensor products of linear operators, Numerical Analysis (math.NA), Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), 15A22, 47A56, 47A80, 47A25, 15A69, 65F15, 15A18, 47B47, Spectral sets of linear operators, Kronecker determinant, Kronecker commutator operator, Multilinear algebra, tensor calculus, two-parameter matrix pencil problem, FOS: Mathematics, Commutators, derivations, elementary operators, etc, Mathematics - Numerical Analysis, Matrix pencils, multiparameter matrix pencil problem, Kronecker canonical form

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2406.17879

On the quadratic two-parameter eigenvalue problem and its linearization

Συγγραφείς: Muhič, Andrej, Plestenjak, Bor

Πηγή: Linear Algebra and its Applications. 432:2529-2542

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, generalized eigenvalue problem, Numerical Analysis, algorithm, Algebra and Number Theory, staircase method, Linearization, model updating, 01 natural sciences, linearisation, Model updating, two-parameter quadratic eigenvalue problem, singular two-parameter eigenvalue problem, Discrete Mathematics and Combinatorics, Singular two-parameter eigenvalue problem, Geometry and Topology, 0101 mathematics, Two-parameter quadratic eigenvalue problem, Kronecker canonical form

Περιγραφή αρχείου: application/xml

A Continuation Method for a Right Definite Two-Parameter Eigenvalue Problem: A continuation method for a right definite two-parameter eigenvalue problem

Συγγραφείς: Bor Plestenjak

Πηγή: SIAM Journal on Matrix Analysis and Applications. 21:1163-1184

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, right definite two-parameter problem, Newton's method, algorithm, convergence, continuation method, Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators, Rayleigh quotient iteration, 0101 mathematics, Numerical solution of eigenvalue problems involving ordinary differential equations, 01 natural sciences, Global methods, including homotopy approaches to the numerical solution of nonlinear equations, Sturm-Liouville problem

Περιγραφή αρχείου: application/xml

Numerical solution of some two-parameter eigenvalue problems

Συγγραφείς: Podlevskyi, B. M.

Πηγή: Journal of Mathematical Sciences. 165:214-220

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, numerical example, iterative algorithm, determinant derivative, Newton method, two-parameter eigenvalue problems, 0101 mathematics, 01 natural sciences, Numerical computation of determinants

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/5677567

Solving eigenvalue problems for two-parameter polynomial matrices. Methods and algorithms. Part I: Solving eigenvalue problems for two-parameter polynomial matrices. Methods and algorithms. I

Συγγραφείς: Kublanovskaya, V. N.

Πηγή: Russian Journal of Numerical Analysis and Mathematical Modelling. 9

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, discrete spectrum, eigenvalue problems, Matrices over function rings in one or more variables, polynomial solutions, minimal null-space basis, singular two-parameter polynomial matrices, 0101 mathematics, 01 natural sciences, rank factorization

Περιγραφή αρχείου: application/xml

Nonlinearizing two-parameter eigenvalue problems

Συγγραφείς: Ringh, Emil, Jarlebring, Elias

Όροι ευρετηρίου: two-parameter eigenvalue problem, nonlinear eigenvalue problem, multiparameter eigenvalue problem, iterative algorithms, implicit function theorem, Computational Mathematics, Beräkningsmatematik, Article in journal, info:eu-repo/semantics/article, text

Σύνδεσμος: http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291995
SIAM Journal on Matrix Analysis and Applications, 0895-4798, 2021, 42:2, s. 775-799

Nonlinearizing two-parameter eigenvalue problems

Συγγραφείς: Ringh, Emil, Jarlebring, Elias

Θεματικοί όροι: Mathematics - Numerical Analysis, 65F15, 15A18, 47J10, 65H17, 15A22, 15A69

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/1907.00913

A Sylvester–Arnoldi type method for the generalized eigenvalue problem with two‐by‐two operator determinants: A Sylvester-Arnoldi type method for the generalized eigenvalue problem with two-by-two operator determinants.

Συγγραφείς: Meerbergen, Karl, Plestenjak, Bor

Συνεισφορές: Axelsson, Owe, Blaheta, Radim, Neytcheva, Maya, Pultarovà, Ivana

Πηγή: Numerical Linear Algebra with Applications. 22:1131-1146

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, Iterative numerical methods for linear systems, Eigenvalues, singular values, and eigenvectors, inverse iteration, Mathematics, Applied, Numerical & Computational Mathematics, separable boundary value problems, algorithms, 01 natural sciences, 7. Clean energy, Arnoldi method, 0102 Applied Mathematics, subspace iteration, 4901 Applied mathematics, Hopf bifurcation, 0101 mathematics, Matlab, operator determinants, low-rank approximation, generalized eigenvalue problem, numerical examples, Science & Technology, 0103 Numerical and Computational Mathematics, Matrix equations and identities, Mathieu's system, Sylvester equation, Bartels-Stewart algorithm, 13. Climate action, Physical Sciences, 4903 Numerical and computational mathematics, Krylov-Schur iterations, Mathematics, two-parameter eigenvalue problem

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://lirias.kuleuven.be/bitstream/123456789/631493/2/MEP_Sylvester9_KM.pdf
https://zbmath.org/6604527
https://doi.org/10.1002/nla.2005
https://lirias.kuleuven.be/handle/123456789/631493
https://doi.org/10.1002/nla.2005

A Jacobi–Davidson method for two‐real‐parameter nonlinear eigenvalue problems arising from delay‐differential equations: A Jacobi-Davidson method for two-real-parameter nonlinear eigenvalue problems arising from delay-differential equations.

Συγγραφείς: Meerbergen, Karl, Schröder, Christian, Voss, Heinrich

Πηγή: Numerical Linear Algebra with Applications. 20:852-868

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, Kronecker products, Stability theory of functional-differential equations, structure-preserving QR-type method, Mathematics, Applied, Numerical & Computational Mathematics, critical delay, 01 natural sciences, Nonlinear eigenvalue problem, Computational methods for sparse matrices, Jacobi-Davidson, 0102 Applied Mathematics, Two-parameter eigenvalue problem, nonlinear eigenvalue problem, delay-differential equation, 4901 Applied mathematics, ALGORITHM, Delay-differential equation, 0101 mathematics, numerical examples, Science & Technology, Critical delay, STABILITY, 0103 Numerical and Computational Mathematics, EIGENPROBLEMS, quadratic eigenvalue problem, Physical Sciences, 4903 Numerical and computational mathematics, Jacobi-Davidson method, Mathematics, two-parameter eigenvalue problem

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://lirias.kuleuven.be/bitstream/123456789/629845/2/nlaa2.pdf

Solving Generalized CDT Problems via Two-Parameter Eigenvalues: Solving generalized CDT problems via two-parameter eigenvalues

Συγγραφείς: Shinsaku Sakaue, Yuji Nakatsukasa, Akiko Takeda, Satoru Iwata 0001

Πηγή: SIAM Journal on Optimization. 26:1669-1694

Θεματικοί όροι: quadratically constrained quadratic programming, Numerical methods based on nonlinear programming, Numerical mathematical programming methods, Nonlinear programming, nonconvex optimization, 0211 other engineering and technologies, 02 engineering and technology, Nonconvex programming, global optimization, Celis-Dennis-Tapia problem, two-parameter eigenvalue problem

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://ora.ox.ac.uk/objects/uuid:86f399cf-b14c-44d6-8377-6ec07729cf86/download_file?safe_filename=Sakaue%2Bet%2Bal%2BSolving%2BGeneralized%2BCDT%2BProblems.pdf&file_format=application%2Fpdf&type_of_work=Journal+article

2固有値問題に対するホモトピー法 / Homotopy Algorithm for Two-Parameter Eigenvalue Problems

Συγγραφείς: Masaaki Shimasaki, 島崎 眞昭

Πηγή: 日本応用数理学会論文誌 / Transactions of the Japan Society for Industrial and Applied Mathematics. 1995, 5(2):121

Numerical Method based on Homotopy Algorithm for Two-Parameter Eigenvalue Problems / ホモトピー法に基づく2固有値問題の数値解法

Συγγραφείς: Masaaki Shimasaki, 島崎 眞昭

Πηγή: 日本応用数理学会論文誌 / Transactions of the Japan Society for Industrial and Applied Mathematics. 1996, 6(3):205

To solving problems of algebra for two-parameter matrices. I: To solving problems of algebra for two-parameter matrices. IV

Συγγραφείς: Kublanovskaya, V. N.

Πηγή: Journal of Mathematical Sciences. 157:731-752

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, Eigenvalues, singular values, and eigenvectors, spectral vectors, Numerical computation of solutions to systems of equations, two-parameter matrices, hereditary pencils, spectral characteristics, algorithms, 01 natural sciences, Factorization of matrices, Matrices over function rings in one or more variables, rank factorizations, spectral problems, 0101 mathematics, polynomial matrix, algorithm, 4. Education, Other matrix algorithms, eigenproblem, spectral problem, Numerical solution of nonlinear eigenvalue and eigenvector problems, two-parameter polynomial matrices, rank factorization method, spectrum points, Numerical computation of roots of polynomial equations, rational matrices, method of hereditary pencils, system of nonlinear algebraic equations, Matrix pencils

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/6300790
https://doi.org/10.1007/s10958-010-9826-z
https://zbmath.org/5632961
https://doi.org/10.1007/s10958-009-9357-7
https://zbmath.org/6110786
https://doi.org/10.1007/s10958-012-0789-0
https://zbmath.org/6300791
https://doi.org/10.1007/s10958-010-9827-y

Newton’s method as a tool for finding the eigenvalues of certain two-parameter (multiparameter) spectral problems: Newton's method as a tool for finding the eigenvalues of certain two-parameter (multiparameter) spectral problems

Συγγραφείς: Podlevskiĭ, B. M.

Πηγή: Computational Mathematics and Mathematical Physics. 48:2140-2145

Θεματικοί όροι: Numerical computation of eigenvalues and eigenvectors of matrices, Iterative numerical methods for linear systems, Newton's method, two-parameter (multiparameter) eigenvalue problems, 0101 mathematics, 01 natural sciences, determinant differentiation

Περιγραφή αρχείου: application/xml

Finding the Set of Branching Points of a Nonlinear Integral Equation Arising in the Synthesis Problem by a Given Power Directivity Pattern

Συγγραφείς: Podlevskyi, Bohdan

Πηγή: 2020 IEEE Ukrainian Microwave Week (UkrMW) Ukrainian Microwave Week (UkrMW), 2020 IEEE. :1-4 Sep, 2020

Relation: 2020 IEEE Ukrainian Microwave Week (UkrMW)

The automatic solution of two-parameter Sturm-Liouville eigenvalue problems in ordinary differential equations

Συγγραφείς: Bailey, Paul B.

Πηγή: Applied Mathematics and Computation. 8:251-259

Θεματικοί όροι: shooting, Ordinary differential operators, two-parameter Sturm-Liouville eigenvalue problems, 0101 mathematics, Numerical solution of eigenvalue problems involving ordinary differential equations, 01 natural sciences, Computer aspects of numerical algorithms

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/3720305
https://doi.org/10.1016/0096-3003(81)90021-7