Accuracy of the Lanczos Process for the Eigenproblem and Solution of Equations

DOI10.1137/17M1133725zbMath1427.65044OpenAlexW2991035998MaRDI QIDQ5203965

Christopher C. Paige

Publication date: 9 December 2019

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

Full work available at URL: https://doi.org/10.1137/17m1133725

zbMATH Keywords

eigenproblemJordan canonical formorthogonalityconjugate gradientssystems of equationsrounding error analysisLanczos processlarge sparse matrices

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Iterative numerical methods for linear systems (65F10) Roundoff error (65G50) Orthogonalization in numerical linear algebra (65F25)

Related Items

When does the Lanczos algorithm compute exactly?, Stability of the Lanczos algorithm on matrices with regular spectral distributions, On the Convergence Rate of Variants of the Conjugate Gradient Algorithm in Finite Precision Arithmetic, Structure in loss of orthogonality, On the cost of iterative computations, Error Bounds for Lanczos-Based Matrix Function Approximation

Uses Software

• LSQR
• MINRES-QLP
• LSMR
• MINRES
• CRAIG

Cites Work

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