Sparse matrices

DOI10.1007/BF01262409zbMath0595.65037MaRDI QIDQ5903172

Khakim D. Ikramov

Publication date: 1986

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

surveyLanczos method

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02)

Uses Software

• symrcm

Cites Work

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• The Lanczos phenomenon - An interpretation based upon conjugate gradient optimization
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Computational methods of linear algebra
• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
• Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices
• The numerically stable reconstruction of a Jacobi matrix from spectral data
• A new iterative method for solution of a large-scale general eigenvalue problem
• Implementation Aspects of Band Lanczos Algorithms for Computation of Eigenvalues of Large Sparse Symmetric Matrices
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• Tracking the Progress of the Lanczos Algorithm for Large Symmetric Eigenproblems
• Solving Sparse Symmetric Generalized Eigenvalue Problems without Factorization
• Simultaneous Iteration for Partial Eigensolution of Real Matrices
• Solution of Sparse Indefinite Systems of Linear Equations
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• Use of the Lanczos Method for Finding Complete Sets of Eigenvalues of Large Sparse Symmetric Matrices
• The Lanczos Algorithm with Selective Orthogonalization
• How to Make the Lanczos Algorithm Converge Slowly
• Computational Variants of the Lanczos Method for the Eigenproblem
• The Solution of Large Symmetric Eigenproblems by Sectioning
• The principle of minimized iterations in the solution of the matrix eigenvalue problem

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