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Rational Interpolation Using Incomplete Barycentric Forms
Author(s) -
Salzer H. E.
Publication year - 1981
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19810610304
Subject(s) - barycentric coordinate system , mathematics , interpolation (computer graphics) , order (exchange) , combinatorics , quotient , linear interpolation , mathematical analysis , geometry , polynomial , physics , motion (physics) , finance , classical mechanics , economics
In rational interpolation of ƒ(x) by (a 0 + a 1 x + … + a n x n )/(1 + b 1 x + … + b m x m ) at x i , i = 1(1)n + m + 1, instead of solving an (n + m + 1)‐th order linear system for a i and b i , we solve only an m‐th order linear system to obtain all n + m + 1 coefficients of 1/(x ‐ x i ) in the “incomplete barycentric form” of the numerator and denominator. The extension to r‐th order osculatory interpolation by (a 0 + a 1 x + … + a nr ‐ 1 x nr ‐ 1 )/(1 + b 1 x + … + b mr x mr ) requires the solution of an rm‐th, instead of the usual (rm + rn)‐th order linear system. In similar treatment of non‐osculatory odd‐point rational trigonometric interpolation by a quotient of trigonometric sums, we solve a 2m‐th, instead of (2n + 2m + 1)‐th order linear system for the coefficients of 1/sin 1/2 (x ‐ x i ).