Precondition Reduced Matrices

By Stephen G. Nash and Ariela Sofer

We study preconditioning strategies for linear systems with positive-definite matrices of the form Z^TZG, where Z is rectangular and G is symmetric but not necessarily positive definite. The preconditioning strategies are designed to be used in the context of a conjugate-gradient iteration, and are suitable within algorithms for constrained optimization problems. The  techniques have other uses, however, and are applied here to a class of problems in the calculus of variations. Numerical tests are also included.

 “Preconditioning Reduced Matrices”, SIAM Journal on Matrix Analysis and Applications, 17 (1996), pp. 47-68.

• Systems Engineering & Operations Research Dept.
• School of Information Technology and Engineering
• George Mason University

(snash@gmu.edu)