Lanczos conjugate-gradient method and pseudoinverse computation on indefinite and singular systems

DOI10.1007/s10957-006-9119-3zbMath1151.65023OpenAlexW2146773115MaRDI QIDQ933807

B. E. Eshmatov

Publication date: 25 July 2008

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-006-9119-3

zbMATH Keywords

unconstrained optimizationKrylov subspace methodssingular matrixMoore-Penrose pseudoinverseindefinite matrixplanar conjugate-gradient method

Mathematics Subject Classification ID

Numerical solutions to overdetermined systems, pseudoinverses (65F20) Numerical mathematical programming methods (65K05) Quadratic programming (90C20) Theory of matrix inversion and generalized inverses (15A09) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (6)

Preconditioning Newton-Krylov methods in nonconvex large scale optimization ⋮ Iterative grossone-based computation of negative curvature directions in large-scale optimization ⋮ An Improvement of the Pivoting Strategy in the Bunch and Kaufman Decomposition, Within Truncated Newton Methods ⋮ Issues on the use of a modified bunch and Kaufman decomposition for large scale Newton's equation ⋮ Planar methods and grossone for the conjugate gradient breakdown in nonlinear programming ⋮ A framework of conjugate direction methods for symmetric linear systems in optimization

Uses Software

• JDQZ

Cites Work

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• Planar conjugate gradient algorithm for large-scale unconstrained optimization. I: Theory
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