Two complementary block Macaulay matrix algorithms to solve multiparameter eigenvalue problems

DOI10.1016/j.laa.2022.08.014zbMath1506.15010OpenAlexW4294862396WikidataQ114151225 ScholiaQ114151225MaRDI QIDQ2080251

Christof Vermeersch, Bart De Moor

Publication date: 7 October 2022

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2022.08.014

zbMATH Keywords

matrix pencilsrealization theorymultiparameter eigenvalue problemsblock Macaulay matrix

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33) Eigenvalues, singular values, and eigenvectors (15A18) Matrix pencils (15A22)

Related Items (1)

Recursive Algorithms to Update a Numerical Basis Matrix of the Null Space of the Block Row, (Banded) Block Toeplitz, and Block Macaulay Matrix

Uses Software

• MultiParEig

Cites Work

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• On the null spaces of the Macaulay matrix
• On linearizations of the quadratic two-parameter eigenvalue problem
• On eigenvalues of rectangular matrices
• Numerical solution of joint eigenpairs of a family of commutative matrices
• Multiparameter eigenvalue problems. Volume I: Matrices and compact operators
• Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem
• A numerical method for the solution of two-parameter eigenvalue problems
• A convergent gradient method for matrix eigenvector-eigentuple problems
• Numerical solution of eigentuple-eigenvector problems in Hilbert spaces by a gradient method
• Multiparameter eigenvalue problems and expansion theorems
• Multivariate polynomial equations with multiple zeros solved by matrix eigenproblems
• Fiber product homotopy method for multiparameter eigenvalue problems
• Least squares optimal realisation of autonomous LTI systems is an eigenvalue problem
• Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems
• The Quadratic Eigenvalue Problem
• A Homotopy Method for Finding All Solutions of a Multiparameter Eigenvalue Problem
• Introduction to Model Spaces and their Operators
• Multiple zeros of nonlinear systems
• On the singular two-parameter eigenvalue problem
• A Numerical Method for the Solution of the Double Eigenvalue Problem
• A Continuation Method for a Right Definite Two-Parameter Eigenvalue Problem
• Multidimensional realisation theory and polynomial system solving
• A Jacobi--Davidson Type Method for the Two-Parameter Eigenvalue Problem
• A Numerical Technique for Multiparameter Eigenvalue Problems
• A Jacobi--Davidson Type Method for a Right Definite Two-Parameter Eigenvalue Problem
• Subspace methods for three‐parameter eigenvalue problems
• The Geometry of Multivariate Polynomial Division and Elimination
• The Conditioning of Linearizations of Matrix Polynomials
• Multiparameter spectral theory and separation of variables
• Multiparameter spectral theory
• Subspace method for multiparameter‐eigenvalue problems based on tensor‐train representations

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