Roy Mathias

Error bounds for the linear complementarity problem with a P-matrix

Abstract We introduce a fundamental quantity associated with a P-matrix and show how this quantity is useful in deriving error bounds for the linear complementarity problem of the P-type. We also obtain (upper and lower) bounds for the quantity introduced.

The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance

This paper presents a small-bulge multishift variation of the multishift QR algorithm that avoids the phenomenon of shift blurring, which retards convergence and limits the number of simultaneous shifts. It replaces the large diagonal bulge in the multishift QR sweep with a chain of many small bulges. The small-bulge multishift QR sweep admits nearly any number of simultaneous shifts---even hundreds---without adverse effects on the convergence rate. With enough simultaneous shifts, the small-bulge multishift QR algorithm takes advantage of the level 3 BLAS, which is a special advantage for computers with advanced architectures.

Perturbation bounds for the polar decomposition

Let

Accurate Eigensystem Computations by Jacobi Methods

M_n ( F )

A Chain Rule for Matrix Functions and Applications

denote the space of matrices over the field F. Given

Cauchy-Schwarz inequalities associated with positive semidefinite matrices

A in M_n ( F )

The Hadamard operator norm of a circulant and applications

define

Quadratic Residual Bounds for the Hermitian Eigenvalue Problem

| A | equiv ( A^ * A )^{1/2}

The spectral norm of a nonnegative matrix

and

An analog of the Cauchy-Schwarz inequality for Hadamard products and unitarily invariant norms

U( A ) equiv A | A |^{ - 1}