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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Symbolic-numeric sparse interpolation of multivariate polynomials
Author(s): Giesbrecht, Mark
Labahn, George
Lee, Wen-shin
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Keywords: Symbolic-numeric computing
multivariate interpolation
Issue Date: 31-Aug-2009
Date Deposited: 3-Nov-2018
Citation: Giesbrecht M, Labahn G & Lee W (2009) Symbolic-numeric sparse interpolation of multivariate polynomials. Journal of Symbolic Computation, 44 (8), pp. 943-959.
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.
DOI Link: 10.1016/j.jsc.2008.11.003
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