The linear algebra of block quasi-Newton algorithms

DOI10.1016/0024-3795(94)90401-4zbMath0861.65044OpenAlexW2084220098MaRDI QIDQ1344059

Dianne P. O'Leary, A. Yu. Yeremin

Publication date: 29 April 1997

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(94)90401-4

zbMATH Keywords

positive definitenesspreconditionerssystems of nonlinear equationsupdate formulasblock conjugate gradient algorithmsblock quasi-Newton algorithmscommon Jacobian matrixleast-change secant propertiesquadratic function minimization

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items (8)

A Seed Method for Solving Nonsymmetric Linear Systems with Multiple Right-hand Sides ⋮ A novel class of approximate inverse preconditioners for large positive definite linear systems in optimization ⋮ Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics ⋮ A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity ⋮ Preconditioners for Krylov subspace methods: An overview ⋮ On solving large-scale limited-memory quasi-Newton equations ⋮ Alternate Broyden’s method for solving linear least squares problem with multiple right-hand sides ⋮ Multiple Schubert’s updating matrix and its compact representation

Cites Work

• Iterative methods for overflow queueing models. I
• Parallel quasi-Newton methods for unconstrained optimization
• Componentwise perturbation theory for linear systems with multiple right- hand sides
• Representations of quasi-Newton matrices and their use in limited memory methods
• Matrix Methods for Queuing Problems
• Least Change Secant Updates for Quasi-Newton Methods
• Optimally conditioned optimization algorithms without line searches
• Quasi-Newton Methods, Motivation and Theory
• Why Broyden’s Nonsymmetric Method Terminates on Linear Equations
• The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations
• A KDF9 ALGOL list-processing scheme

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