Iterative Solution of Indefinite Symmetric Linear Systems by Methods Using Orthogonal Polynomials over Two Disjoint Intervals

DOI10.1137/0720052zbMath0547.65028OpenAlexW2093972066MaRDI QIDQ3339175

Yousef Saad

Publication date: 1983

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0720052

zbMATH Keywords

comparisonconvergenceChebyshev polynomialsorthogonal polynomialsNumerical experimentsindefinite symmetric linear systemsLanczos algorithmconjugate gradientChebyshev semi-iterative methodSYMMLQ algorithmadaptive parameter estimationconjugate residual methodslarge invertible symmetric matrixRayleigh-Ritz type estimates

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Iterative numerical methods for linear systems (65F10)

Related Items (12)

Rayleigh-Ritz and Lanczos methods for symmetric matrix pencils ⋮ On the application of orthogonal polynomials to the iterative solution of linear systems of equations with indefinite or non-Hermitian matrices ⋮ Matrix-free polynomial-based nonlinear least squares optimized preconditioning and its application to discontinuous Galerkin discretizations of the Euler equations ⋮ An adaptive Richardson iteration method for indefinite linear systems ⋮ Iterative methods for the computation of a few eigenvalues of a large symmetric matrix ⋮ Tensor Equivalents for Solution of Linear Systems: A Parallel Algorithm ⋮ A new approach to the generalized trace formula and asymptotics of Turán's determinant for polynomials with asymptotically \(N\)-periodic recurrence coefficients ⋮ An adaptive method for solving nonsymmetric linear systems involving applications of SCPACK ⋮ Claculating interior eigenvalues and eigenvectors with an implicitly restarted and a filter diagonalization method ⋮ Computing Partial Spectra with Least-Squares Rational Filters ⋮ Orthogonal Polynomials on Several Intervals Via a Polynomial Mapping ⋮ A hybrid iterative method for symmetric indefinite linear systems

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