Rank-one and Rank-two Corrections to Positive Definite Matrices Expressed in Product Form

DOI10.1093/imamat/11.1.73zbMath0252.15007OpenAlexW1963750522WikidataQ59904555 ScholiaQ59904555MaRDI QIDQ5665296

A. R. Gourlay, K. W. Brodlie, John Greenstadt

Publication date: 1973

Published in: IMA Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/imamat/11.1.73

Mathematics Subject Classification ID

Nonlinear programming (90C30) Matrix equations and identities (15A24) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items

Factorized Variable Metric Methods for Unconstrained Optimization, A strict bound to the condition number of bordered positive definite matrices, Inertia-preserving secant updates, A quasi-Newton based pattern search algorithm for unconstrained optimization, Parallel quasi-Newton methods for unconstrained optimization, Performance of various BFGS implementations with limited precision second-order information, Hybrid methods for large sparse nonlinear least squares, Solutions to 18 constrained optimization problems on the rank and inertia of the linear matrix function, Some practical procedures for the solution of nonlinear finite element equations, Direct Secant Updates of Matrix Factorizations, Updating conjugate directions by the BFGS formula, A new quasi-Newton pattern search method based on symmetric rank-one update for unconstrained optimization, Optimally conditioned optimization algorithms without line searches, Updating of conjugate direction matrices using members of Broyden's family, A bound to the condition number of canonical rank-two corrections and applications to the variable metric method, On some classes of variationally derived quasi-Newton methods for systems of nonlinear algebraic equations, Generation of classes of symmetric rank-2 secant updates and the maximality of the Davidon class, Unnamed Item, On the symmetric rank-m correction of matrices, On averaging and representation properties of the BFGS and related secant updates, Optimal conditioning in the convex class of rank two updates, Variable metric methods for linearly constrained nonlinear minimax approximation, An arc length control procedure to solve parabolic problems