Accurate eigenvalues and exact zero Jordan blocks of totally nonnegative matrices

DOI10.1007/s00211-019-01022-0zbMath1434.65035OpenAlexW2910998582WikidataQ128625275 ScholiaQ128625275MaRDI QIDQ1728086

Plamen Koev

Publication date: 21 February 2019

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-019-01022-0

zbMATH Keywords

eigenvaluestotally nonnegative matricesHilbert matrixill-conditioned matricesPascal matrixsingular value problemexact zero Jordan blocksfloating point arithmeticsmachine precisionnonnegative bidiagonal decompositionsubtractive cancellation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Ill-posedness and regularization problems in numerical linear algebra (65F22) Eigenvalues, singular values, and eigenvectors (15A18) Numerical computation of matrix norms, conditioning, scaling (65F35) Numerical algorithms for computer arithmetic, etc. (65Y04) Diagonalization, Jordan forms (15A20)

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Uses Software

• LAPACK
• Matlab
• TNTool

Cites Work

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• Total positivity and Neville elimination
• Some properties of totally positive matrices
• A reduction theorem for totally positive matrices
• Accurate Singular Values of Bidiagonal Matrices
• Accurate Computations with Totally Nonnegative Matrices
• LAPACK Users' Guide
• Bidiagonal Factorizations of Totally Nonnegative Matrices
• Jordan Structures of Totally Nonnegative Matrices
• Accurate Singular Value Decompositions of Structured Matrices
• Accurate Eigenvalues and SVDs of Totally Nonnegative Matrices
• Totally positive matrices