A bootstrap method for sum-of-poles approximations

A bootstrap method is presented for finding efficient sum-of-poles approximations of causal functions. The method is based on a recursive application of the nonlinear least squares optimization scheme developed in (Alpert et al. in SIAM J. Numer. Anal. 37:1138–1164, 2000), followed by the balanced truncation method for model reduction in computational control theory as a final optimization step. The method is expected to be useful for a fairly large class of causal functions encountered in engineering and applied physics. The performance of the method and its application to computational physics are illustrated via several numerical examples

Latent Roots and Latent Vectors

This book is concerned with the latent roots and latent vectors of matrices whose elements are real. Its main purpose is to discuss some of the methods available for finding latent roots and vectors. The methods presented include not only those that are the most useful in practice, but some chosen because of the interesting ideas they present and the help they give to a general understanding of the latent root and vector problem. I have attempted throughout to introduce the material in as uncomplicated a manner as possible

Case Studies on The Development of ScaLAPACK and the NAG Numerical PVM Library

In this paper we look at the development of ScaLAPACK, a software library for dense and banded numerical linear algebra, and the NAG Numerical PVM Library, which includes software for dense and sparse linear algebra, quadrature, optimization and random number generation. Both libraries are aimed at distributed memory machines, including networks of workstations. The paper concentrates on the underlying design and the testing of the libraries. Keywords BLAS, LAPACK, NAG, numerical libraries, numerical linear algebra, numerical software, ScaLAPACK 2 Case Studies on The Development of ScaLAPACK and the NAG Numerical PVM Library 1 INTRODUCTION This paper looks at the development of two software libraries aimed at distributed memory machines, ScaLAPACK and the NAG Numerical PVM Library y , concentrating on the underlying design of the libraries and issues concerned with testing the components of the libraries. The development of ScaLAPACK, and related software, had a strong influen..