%0 Journal Article
%J Linear Algebra and its Applications
%D 1994
%T The linear algebra of block quasi-newton algorithms
%A O'Leary, Dianne P.
%A Yeremin,A.
%X The quasi-Newton family of algorithms for minimizing functions and solving systems of nonlinear equations has achieved a great deal of computational success and forms the core of many software libraries for solving these problems. In this work we extend the theory of the quasi-Newton algorithms to the block case, in which we minimize a collection of functions having a common Hessian matrix, or we solve a collection of nonlinear equations having a common Jacobian matrix. This paper focuses on the linear algebra: update formulas, positive definiteness, least-change secant properties, relation to block conjugate gradient algorithms, finite termination for quadratic function minimization or solving linear systems, and the use of the quasi-Newton matrices as preconditioners.
%B Linear Algebra and its Applications
%V 212–213
%P 153 - 168
%8 1994/11/15/
%@ 0024-3795
%G eng
%U http://www.sciencedirect.com/science/article/pii/0024379594904014
%R 10.1016/0024-3795(94)90401-4