The polynomial numerical hulls of Jordan blocks and related matrices.

DOI10.1016/S0024-3795(03)00615-3zbMath1044.15019MaRDI QIDQ1414161

Vance Faber, Anne Greenbaum, Donald E. Marshall

Publication date: 19 November 2003

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

zbMATH Keywords

eigenvalueToeplitz matrixJordan blockspolynomial numerical hullnonnormal matrix

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical computation of matrix norms, conditioning, scaling (65F35) Canonical forms, reductions, classification (15A21)

Related Items (14)

Characterizations of the polynomial numerical hull of degree \(k\) ⋮ Linear preservers of polynomial numerical hulls of matrices ⋮ GMRES algorithms over 35 years ⋮ Polynomial numerical hulls of the direct sum of a normal matrix and a Jordan block ⋮ New conditions for non-stagnation of minimal residual methods ⋮ Field of values of perturbed matrices and quantum states ⋮ Upper and lower bounds on norms of functions of matrices ⋮ Convergence analysis of Krylov subspace methods ⋮ Polynomial numerical hulls of matrix polynomials, II ⋮ Linear maps preserving the polynomial numerical radius of matrices ⋮ A new investigation of the extended Krylov subspace method for matrix function evaluations ⋮ Linear maps compressing the polynomial numerical hulls of matrices ⋮ Computing the Spectrum and Representing the Resolvent ⋮ Polynomial numerical hulls of the direct sum of two Jordan blocks

Uses Software

• Pseudospectra

Cites Work

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• Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
• The commutant lifting approach to interpolation problems
• Introduction to large truncated Toeplitz matrices
• Generalizations of the field of values useful in the study of polynomial functions of a matrix
• Card Shuffling and the Polynomial Numerical Hull of Degree k
• Hessenberg matrices in krylov subspaces and the computation of the spectrum

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