On Efficient Numerical Approximation of the Bilinear Form $c^*A^{-1}b$

DOI10.1137/090753723zbMath1227.65033OpenAlexW2029578359MaRDI QIDQ3095074

Petr Tichý, Zdeněk Strakoš

Publication date: 28 October 2011

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/090753723

zbMATH Keywords

numerical experimentsconjugate gradient methodbilinear formsmodel reductionscattering amplitudeKrylov subspace methodsLanczos algorithmArnoldi algorithmmethod of momentsbiconjugate gradient methodGauss-Christoffel quadrature

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Quadratic and bilinear forms, inner products (15A63)

Related Items (9)

Estimation of the bilinear form \(y^\ast f(A)x\) for Hermitian matrices ⋮ New matrix function approximations and quadrature rules based on the Arnoldi process ⋮ A two-sided short-recurrence extended Krylov subspace method for nonsymmetric matrices and its relation to rational moment matching ⋮ A literature survey of matrix methods for data science ⋮ Towards backward perturbation bounds for approximate dual Krylov subspaces ⋮ Block conjugate gradient type methods for the approximation of bilinear form \(C^HA^{-1}B\) ⋮ Goal-oriented mesh adaptation method for nonlinear problems including algebraic errors ⋮ On efficient numerical solution of linear algebraic systems arising in goal-oriented error estimates ⋮ Preconditioned Multishift BiCG for $\mathcal{H}_2$-Optimal Model Reduction

Uses Software

• LSQR
• CGS

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