Fast and Stable Algorithms for Banded Plus Semiseparable Systems of Linear Equations

DOI10.1137/S0895479899353373zbMath1050.65023OpenAlexW1983483574MaRDI QIDQ4443831

Ming Gu, Shivkumar Chandrasekaran

Publication date: 19 January 2004

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0895479899353373

zbMATH Keywords

numerical resultsfast algorithmsstable algorithmsdirect methodsbordered matrixmatrix factorizationbanded matrixsemiseparable matrix\({\mathcal H}\)-matrix

Mathematics Subject Classification ID

Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09) Direct numerical methods for linear systems and matrix inversion (65F05)

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A fast direct solver for scattering problems involving elongated structures ⋮ Stability of QR-based fast system solvers for a subclass of quasiseparable rank one matrices ⋮ Inverses of generalized Hessenberg matrices ⋮ Exact computations with quasiseparable matrices ⋮ A Levinson-like algorithm for symmetric strongly nonsingular higher order semiseparable plus band matrices ⋮ A brief introduction to pseudo-spectral methods: application to diffusion problems ⋮ Orthogonal basis functions in discrete least-squares rational approximation. ⋮ Two fast algorithms for solving diagonal-plus-semiseparable linear systems. ⋮ Generalized Rybicki Press algorithm ⋮ Newton-Krylov solvers for the equation-free computation of coarse traveling waves ⋮ A high-order accurate accelerated direct solver for acoustic scattering from surfaces

Uses Software

• LAPACK
• Matlab