Book Review: Interpolation of rational matrix functions
نویسندگان
چکیده
منابع مشابه
Sparse interpolation of multivariate rational functions
Consider the black box interpolation of a τ -sparse, n-variate rational function f , where τ is the maximum number of terms in either numerator or denominator. When numerator and denominator are at most of degree d, then the number of possible terms in f is O(dn) and explodes exponentially as the number of variables increases. The complexity of our sparse rational interpolation algorithm does n...
متن کاملMatrix Rational Interpolation with Poles as Interpolation Points
In this paper, we show the equivalence between matrix rational interpolation problems with poles as interpolation points and no-pole problems. This equivalence provides an effective method for computing matrix rational interpolants having poles as interpolation points. However, this equivalence is only valid in those cases where enough pole information is known. It is an open problem on how one...
متن کاملTriangular C Interpolation by Rational Functions
Two general local C triangular interpolation schemes by rational functions from C data are proposed for any nonnegative integer m. The schemes can have either 2m + 1 order algebraic precision if the required data are given on vertices and edges, or m + E[m/2] + 1 or m + 1 order algebraic precision if the data are given only at vertices. The orders of the interpolation error are estimated. Examp...
متن کاملA Duality in Interpolation to Analytic Functions by Rational Functions.
omission and to say whether its correction will lead only to a new interpretation of the constants of our equations or to an actual change of their form. Another simplification is the neglect of polar and excited states: While there is reason to assume that their influence is small, its exact estimate is still lacking. Further inaccuracies were discussed in our preceding paper: The use of Bloch...
متن کاملConvergence of Linear Barycentric Rational Interpolation for Analytic Functions
Polynomial interpolation to analytic functions can be very accurate, depending on the distribution of the interpolation nodes. However, in equispaced nodes and the like, besides being badly conditioned, these interpolants fail to converge even in exact arithmetic in some cases. Linear barycentric rational interpolation with the weights presented by Floater and Hormann can be viewed as blended p...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1993
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1993-00386-0