Fixing multiple eigenvalues by a minimal perturbation

DOI10.1016/j.laa.2009.11.030zbMath1188.65050OpenAlexW2087291145MaRDI QIDQ2267409

Ross A. Lippert

Publication date: 1 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2009.11.030

zbMATH Keywords

inverse eigenvalue problemspectral normeigenvalue perturbationsingular value perturbation

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Numerical solutions to inverse eigenvalue problems (65F18)

Related Items (6)

Nearest linearly structured polynomial matrix with some prescribed distinct eigenvalues ⋮ On the distance from a matrix polynomial to matrix polynomials with some prescribed eigenvalues ⋮ Perturbation analysis on matrix pencils for two specified eigenpairs of a semisimple eigenvalue with multiplicity two ⋮ Nearest matrix with prescribed eigenvalues and its applications ⋮ On the distance from a matrix polynomial to matrix polynomials with k prescribed distinct eigenvalues ⋮ Nearest matrix with a prescribed eigenvalue of bounded multiplicities

Uses Software

• PHCpack
• JDQR
• JDQZ

Cites Work

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• Numerical computation of an analytic singular value decomposition of a matrix valued function
• Nearest matrix with two prescribed eigenvalues
• A formula for the 2-norm distance from a matrix to the set of matrices with multiple eigenvalues
• Normal matrices and an extension of Malyshev's formula
• Singular values and invariant factors of matrix sums and products
• The dimension of matrices (matrix pencils) with given Jordan (Kronecker) canonical forms
• Fixing two eigenvalues by a minimal perturbation
• Nonsmooth analysis of singular values. I: Theory
• Nonsmooth analysis of singular values. II: Applications
• The Weyr Characteristic
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS
• Generalized Gradients and Applications
• A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm
• The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part I
• Inverse Eigenvalue Problems
• Algorithm 795
• The Interplay of Ranks of Submatrices

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