Because of their versatility and robustness, numerical continuation or path following
methods have been finding ever wider use in scientific applications. Our aim here is to give …

Completely revised text focuses on use of spectral methods to solve boundary value,
eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational …

Over the past fifteen years two new techniques have yielded extremely important
contributions toward the numerical solution of nonlinear systems of equations. This book …

This book was intended as an introduction to the topic of numerical continuation which
would be accessible to a readership of widely varying mathematical backgrounds. Realizing …

This work is aimed at mathematics and engineering graduate students and researchers in
the areas of optimization, dynamical systems, control sys tems, signal processing, and linear …

We establish a number of properties associated with the dynamical system H ̇=[H,[H, N]],
where H and N are symmetric n by n matrices and [A, B]= AB− BA. The most important of …

Inverse eigenvalue problems arise in a remarkable variety of applications and associated
with any inverse eigenvalue problem are two fundamental questions—the theoretical issue …

A collection of inverse eigenvalue problems are identified and classified according to their
characteristics. Current developments in both the theoretic and the algorithmic aspects are …

The main ideas of path following by predictor–corrector and piecewise-linear methods, and
their application in the direction of homotopy methods and nonlinear eigenvalue problems …

We review the most important theoretical results on Newton's method concerning the
convergence properties, the error estimates, the numerical stability and the computational …