Share This Article:

Fast and Numerically Stable Approximate Solution of Trummer’s Problem

Full-Text HTML XML Download Download as PDF (Size:2567KB) PP. 387-395
DOI: 10.4236/ajcm.2014.45033    2,509 Downloads   3,164 Views

ABSTRACT

Trummer’s problem is the problem of multiplication of an n × n Cauchy matrix C by a vector. It serves as the basis for the solution of several problems in scientific computing and engineering [1]. The straightforward algorithm solves Trummer’s problem in O(n2) flops. The fast algorithm solves the problem in O(nlog2n) flops [2] but has poor numerical stability. The algorithm we discuss here in this paper is the celebrated multipoint algorithm [3] which has been studied by Pan et al. The algorithm approximates the solution in O(nlogn) flops in terms of n but its cost estimate depends on the bound of the approximation error and also depends on the correlation between the entries of the pair of n-dimensional vectors defining the input matrix C.

Cite this paper

Tabanjeh, M. (2014) Fast and Numerically Stable Approximate Solution of Trummer’s Problem. American Journal of Computational Mathematics, 4, 387-395. doi: 10.4236/ajcm.2014.45033.

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.