
Accession Number : ADA327603
Title : What Hadamard Missed,
Corporate Author : CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS
Personal Author(s) : Parlett, Beresford N.
PDF Url : ADA327603
Report Date : MAR 1996
Pagination or Media Count : 25
Abstract : Consider the task of finding all the eigenvalues of a dense matrix. We show how Hadamard's procedure (1891) can be organized into Aitken's Htable (1925) and how the Htable may be transformed into Rutishauser's qdarray (1953) with the help of the Lanczos algorithm. We show how the qd algorithm can be interpreted as defining the LR algorithm (1958). Finally we show how the original qd algorithm may be transformed into the shifted differential qd algorithm dqds developed by Fernando and Parlett (1993/94). The Lanczos algorithm takes a dense matrix into tridiagonal form and then dqds is a fast and accurate procedure for extracting the eigenvalues.
Descriptors : *MATRICES(MATHEMATICS), *EIGENVALUES, ALGORITHMS, PARALLEL PROCESSING, MAPPING(TRANSFORMATIONS).
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE