Ritz values of normal matrices and Ceva's theorem

DOI10.1016/j.laa.2012.12.030zbMath1305.15026OpenAlexW1969133863MaRDI QIDQ389685

Derek J. Hansen, Russell L. Carden

Publication date: 21 January 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.12.030

zbMATH Keywords

eigenvaluesRitz valuesnormal matricesinterlacingCeva's theoremrestarted Arnoldi method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Inverse problems in linear algebra (15A29) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (4)

Interaction between Hermitian and normal imbeddings ⋮ Continuity of submatrices and Ritz sets associated to a point in the numerical range ⋮ An Inverse Problem for the $k$-Rank Numerical Range ⋮ Location of Ritz values in the numerical range of normal matrices

Uses Software

• IRAM

Cites Work

• Imbedding conditions for normal matrices
• Principal submatrices of normal and Hermitian matrices
• A method for the inverse numerical range problem
• Imbedding Conditions for Hermitian and Normal Matrices
• Generalized minimax and interlacing theorems
• An inverse field of values problem
• A simple algorithm for the inverse field of values problem
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• Numerical Determination of the Field of Values of a General Complex Matrix
• Numerical Optimization
• GMRES/CR and Arnoldi/Lanczos as Matrix Approximation Problems
• The Tortoise and the Hare Restart GMRES
• Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES
• Ritz Value Localization for Non-Hermitian Matrices
• The Arnoldi Eigenvalue Iteration with Exact Shifts Can Fail
• Inverse spectral problem for normal matrices and the Gauss-Lucas theorem
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