Topics in the numerical linear algebra of Toeplitz and Hankel matrices

DOI10.1002/gamm.201490009zbMath1093.47028OpenAlexW1491497439MaRDI QIDQ4681596

Karla Rost, Albrecht Böttcher

Publication date: 24 June 2005

Published in: GAMM-Mitteilungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/gamm.201490009

zbMATH Keywords

eigenvaluesinversion formulaToeplitz matrixHankel matrixfast algorithmBezoutian

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Theory of matrix inversion and generalized inverses (15A09) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (2)

Numerical Linear Algebra for Model Reduction in Control and Simulation ⋮ Structured Eigenvalue Problems

Uses Software

• mctoolbox
• Eigtool

Cites Work

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• Split algorithms for skewsymmetric Toeplitz matrices with arbitrary rank profile
• On the inverses of Toeplitz-plus-Hankel matrices
• DFT representations of Toeplitz-plus-Hankel Bézoutians with application to fast matrix-vector multiplication
• Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
• On Szegö's eigenvalue distribution theorem and non-Hermitian kernels
• Asymptotic behavior of block Toeplitz matrices and determinants. II
• Pseudospectra and singular values of large convolution operators
• Centro-symmetric and centro-skewsymmetric Toeplitz matrices and Bézoutians
• Asymptotic spectra of dense Toeplitz matrices are unstable
• Fast algorithms for centro-symmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices
• Centrosymmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices and Bézoutians
• Split algorithms for Hermitian Toeplitz matrices with arbitrary rank profile
• Algebras of higher dimension for displacement decompositions and computations with Toeplitz plus Hankel matrices
• The Toeplitz Matrices of an Arbitrary Laurent Polynomial.
• Structured condition numbers of large Toeplitz matrices are rarely better than usual condition numbers
• Split algorithms for symmetric Toeplitz matrices with arbitrary rank profile
• Lower bounds for the absolute value of random polynomials on a neighborhood of the unit circle
• Structured Perturbations Part I: Normwise Distances
• More on Electrostatic Models for Zeros of Orthagonal Polynomials
• New Fast Algorithms for Toeplitz-Plus-Hankel Matrices
• Computationally Efficient Reduced Polynomial Based Algorithms for Hermitian Toeplitz Matrices
• Piecewise Continuous Toeplitz Matrices and Operators: Slow Approach to Infinity
• Integral equations on a half-line with kernel depending upon the difference of the arguments
• Chebyshev-Hankel matrices and the splitting approach for centrosymmetric Toeplitz-plus-Hankel matrices
• A two-step even-odd split Levinson algorithm for Toeplitz systems

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