On the closed representation for the inverses of Hessenberg matrices

DOI10.1016/j.cam.2011.07.008zbMath1237.15005OpenAlexW2029499835MaRDI QIDQ415211

J. Abderramán Marrero, Venancio Tomeo

Publication date: 11 May 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.07.008

zbMATH Keywords

inverse matrixresolvent matrixHessenberg matrixgeneral orthogonal polynomialsHessenbergianlower semiseparable (plus diagonal) matrix

Mathematics Subject Classification ID

Theory of matrix inversion and generalized inverses (15A09) Determinants, permanents, traces, other special matrix functions (15A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Spectrum, resolvent (47A10) Special sequences and polynomials (11B83) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

On the factorization and the inverse of a tridiagonal matrix ⋮ Inverses of generalized Hessenberg matrices ⋮ Unnamed Item ⋮ On inverses of infinite Hessenberg matrices ⋮ Some results on determinants and inverses of nonsingular pentadiagonal matrices ⋮ Explicit inversion formulas for properly Hessenberg and Toeplitz–Hessenberg matrices ⋮ Non-symbolic algorithms for the inversion of tridiagonal matrices ⋮ On new algorithms for inverting Hessenberg matrices ⋮ Hybrid Ikebe-Newton's iteration for inverting general nonsingular Hessenberg matrices ⋮ On compact representations for the solutions of linear difference equations with variable coefficients ⋮ Inverses and determinants of Toeplitz-Hessenberg matrices

Cites Work

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• A Fast Björck–Pereyra-Type Algorithm for Solving Hessenberg-Quasiseparable-Vandermonde Systems
• A fast algorithm for computing the smallest eigenvalue of a symmetric positive-definite Toeplitz matrix
• Analytical inversion of general tridiagonal matrices
• The Interplay of Ranks of Submatrices
• Methods of inverting tridiagonal matrices
• On the Solution of a Linear Homogeneous Difference Equation with Variable Coefficients
• Structures preserved by matrix inversion
• A bibliography on semiseparable matrices
• The inverse of a tridiagonal matrix

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