An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices

DOI10.1016/0021-9991(88)90067-8zbMath0619.65027OpenAlexW2011000353MaRDI QIDQ1089736

Giuseppe Gambolati, Giorgio Pini, Flavio Sartoretto

Publication date: 1988

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9991(88)90067-8

zbMATH Keywords

convergence accelerationnumerical experimentseigenvectorsRayleigh quotientpreconditioning matricesincomplete Cholesky factorizationconjugate gradient schemeaccelerated optimization techniquefinite element symmetric positive definite matricesleftmost eigenvaluesstepwise deflation procedurevery fast convergence rate

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element methods applied to problems in solid mechanics (74S05) Numerical computation of matrix norms, conditioning, scaling (65F35)

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CONJUGATE GRADIENT METHODS FOR SOLVING THE SMALLEST EIGENPAIR OF LARGE SYMMETRIC EIGENVALUE PROBLEMS, LEFTMOST EIGENVALUE OF REAL AND COMPLEX SPARSE MATRICES ON PARALLEL COMPUTER USING APPROXIMATE INVERSE PRECONDITIONING, Accelerated simultaneous iterations for large finite element eigenproblems, On vectorizing the preconditioned generalized conjugate residual methods, Computation of minimum eigenvalue through minimization of rayleigh's quotient for large sparse matrices using vector computer:, Block subspace projection preconditioned conjugate gradient method in modal structural analysis, An orthogonal accelerated deflation technique for large symmetric eigenproblems, Efficient parallel solution to large‐size sparse eigenproblems with block FSAI preconditioning, Numerical comparison of preconditionings for large sparse finite element problems

Cites Work

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• The eigenvalue problem \((A-\lambda B)x = 0\) for symmetric matrices of high order
• Extreme eigenvalues of large sparse matrices by Rayleigh quotient and modified conjugate gradients
• Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations
• Simultaneous Rayleigh-quotient minimization methods for Ax=lambdaBx
• Preconditioned iterative methods for the large sparse symmetric eigenvalue problem
• Numerical integration of differential equations and large linear systems. Proceedings of two Workshops held at the University of Bielefeld, Spring 1980
• Iterative eigenvalue algorithms based on convergent splittings
• A class of iterative methods for finite element equations
• The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
• Minimal eigenvalue of large sparse matrices by an efficient reverse power-conjugate gradient scheme
• New iterative methods for solution of the eigenproblem
• An iterative procedure for the calculation of the lowest real eigenvalue and eigenvector of a nonsymmetric matrix
• Acceleration of the convergence in Nesbet's algorithm for eigenvalues and eigenvectors of large matrices
• The iterative calculation of several of the lowest or highest eigenvalues and corresponding eigenvectors of very large symmetric matrices
• A robust incomplete Choleski-conjugate gradient algorithm
• Solution of the partial eigenproblem by iterative methods
• A numerical study of various algorithms related to the preconditioned conjugate gradient method
• Fast solution to finite element flow equations by newton iteration and modified conjugate gradient method
• Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods
• A Trace Minimization Algorithm for the Generalized Eigenvalue Problem
• 𝑆𝑂𝑅-methods for the eigenvalue problem with large sparse matrices
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• Gradient methods for finite-element eigenproblems.
• The computational efficiency of a new minimization algorithm for eigenvalue analysis
• Optimal gradient minimization scheme for finite element eigenproblems
• Berechnung von Eigenwerten und Eigenvektoren normaler Matrizenpaare durch Ritz‐Iteration
• Methods of conjugate gradients for solving linear systems