Nearest matrix with two prescribed eigenvalues

DOI10.1016/j.laa.2004.07.002zbMath1074.15011OpenAlexW2127340547MaRDI QIDQ1779396

Juan-Miguel Gracia

Publication date: 1 June 2005

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

Full work available at URL: https://doi.org/10.1016/j.laa.2004.07.002

zbMATH Keywords

prescribed eigenvaluesdistancesingular valuesspectral normnearest matrixanalytic matrix functionWilkinson's problem

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Conditioning of matrices (15A12)

Related Items (11)

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 ⋮ Fixing multiple eigenvalues by a minimal perturbation ⋮ On the distance from a weakly normal matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue ⋮ Nearest southeast submatrix that makes multiple a prescribed eigenvalue. ⋮ Computational aspect to the nearest matrix with two prescribed eigenvalues ⋮ A unified approach to computing the nearest complex polynomial with a given zero

Cites Work

• Inertia characteristics of self-adjoint matrix polynomials
• A formula for the 2-norm distance from a matrix to the set of matrices with multiple eigenvalues
• A formula for computation of the real stability radius
• Singular values and invariant factors of matrix sums and products
• Safety neighbournoods for the invariants of the matrix similarity^∗
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