@article {15820,
title = {The linear algebra of block quasi-newton algorithms},
journal = {Linear Algebra and its Applications},
volume = {212{\textendash}213},
year = {1994},
month = {1994/11/15/},
pages = {153 - 168},
abstract = {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.},
isbn = {0024-3795},
doi = {10.1016/0024-3795(94)90401-4},
url = {http://www.sciencedirect.com/science/article/pii/0024379594904014},
author = {O{\textquoteright}Leary, Dianne P. and Yeremin,A.}
}