Comments on “On the Polynomial Multiplication in Chebyshev Form”

Park, Sun-Mi; Chang, Ku-Young; Hong, Dowon; Seo, Changho

doi:10.1109/tc.2013.179

Cited by 1 publication

(1 citation statement)

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“…Another area of improvement would concern the binary product operation, whose complexity currently scales exponentially in the number of variables and the expansion order. Several studies have explored approaches to speeding up the multiplication of univariate and bivariate polynomials in Chebyshev basis (e.g., [2,5,22,45]). Ways to use some of these developments for multivariate Chebyshev polynomials could be explored as part of future work.…”

Section: Discussionmentioning

confidence: 99%

Chebyshev model arithmetic for factorable functions

et al. 2016

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This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden.

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Section: Discussionmentioning

confidence: 99%