On the permissible arrangements of Ritz values for normal matrices in the complex plane

DOI10.1016/j.laa.2013.02.014zbMath1281.15007OpenAlexW2064275080MaRDI QIDQ393373

Zvonimir Bujanović

Publication date: 17 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.2013.02.014

zbMATH Keywords

convergenceeigenvaluesRitz valuesArnoldi algorithmnormal matrixKrylov subspacesharmonic Ritz valuesCauchy matrix

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Inverse problems in linear algebra (15A29) Numerical solutions to inverse eigenvalue problems (65F18)

Related Items (3)

The Coefficients of the FOM and GMRES Residual Polynomials ⋮ Continuity of submatrices and Ritz sets associated to a point in the numerical range ⋮ Location of Ritz values in the numerical range of normal matrices

Uses Software

• MPT
• IRAM

Cites Work

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• Computing interior eigenvalues of large matrices
• Imbedding conditions for normal matrices
• A Krylov--Schur Algorithm for Large Eigenproblems
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES
• The Arnoldi Eigenvalue Iteration with Exact Shifts Can Fail
• Hybrid Systems: Computation and Control
• Inverse spectral problem for normal matrices and the Gauss-Lucas theorem

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