This book evolved from lecture notes developed over the past 20+ years of teaching this
material, mostly in Applied Mathematics 585–6 at the University of Washington. The course …

Assume that after preconditioning we are given a fixed point problem x= Lx+ f (*) where L is
a bounded linear operator which is not assumed to be symmetric and f is a given vector. The …

It is well known that a necessary condition for the Lax-stability of the method of lines is that
the eigenvalues of the spatial discretization operator, scaled by the time step k, lie within a …

Optimization problems involving the eigenvalues of symmetric and nonsymmetric matrices
present a fascinating mathematical challenge. Such problems arise often in theory and …

The integration of semidiscrete approximations for time-dependent problems is encountered
in a variety of applications. The Runge--Kutta (RK) methods are widely used to integrate the …

This article addresses the general problem of establishing upper bounds for the norms of the
nth powers of square matrices. The focus is on upper bounds that grow only moderately (or …

Accurate modeling of the interaction between convective and diffusive processes is one of
the most common challenges in the numerical approximation of partial differential equations …

For a given square matrix A and positive integer k, we consider sets Ω in the complex plane
satisfying [Formula: see text] for all polynomials p of degree k or less. The largest such set …

We survey results related to the Kreiss Matrix Theorem, especially examining extensions of
this theorem to Banach space and Hilbert space. The survey includes recent and …

Analysis of nonsymmetric matrix iterations based on eigenvalues can be misleading. In this
paper, we discuss sixteen theorems involving ε\defΛ\defλ-pseudospectra that each …