Publication
Title
Symbolic-numeric sparse interpolation of multivariate polynomials
Author
Abstract
We consider the problem of sparse interpolation of an approximate multivariate black-box polynomial in floating point arithmetic. That is, both the inputs and outputs of the black-box polynomial have some error, and all numbers are represented in standard, fixed-precision, floating point arithmetic. By interpolating the black box evaluated at random primitive roots of unity, we give efficient and numerically robust Solutions. We note the similarity between the exact Ben-Or/Tiwari sparse interpolation algorithm and the classical Prony's method for interpolating a sum of exponential functions, and exploit the generalized eigenvalue reformulation of Prony's method. We analyse the numerical stability of our algorithms and the sensitivity of the Solutions, as well as the expected conditioning achieved through randomization. Finally, we demonstrate the effectiveness of our techniques in practice through numerical experiments and applications. (C) 2008 Elsevier Ltd. All rights reserved.
Language
English
Source (journal)
Journal of symbolic computation. - London
Publication
London : 2009
ISSN
0747-7171
Volume/pages
44:8(2009), p. 943-959
ISI
000266514800001
Full text (Publisher's DOI)
Full text (open access)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identification
Creation 24.02.2012
Last edited 15.07.2017
To cite this reference