Bivariate polynomial and continued fraction interpolation over ortho-triples |
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Authors: | Ren-Hong WangJiang Qian |
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Affiliation: | a School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China b College of Sciences, Hohai University, Nanjing 210098, China |
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Abstract: | By means of the barycentric coordinates expression of the interpolating polynomial over each ortho-triple, some properties are obtained. Moreover, the explicit coefficients in terms of B-net for one ortho-triple, and two ortho-triples are worked out, respectively. Thus the computation of multiple integrals can be converted into the sum of the coefficients in terms of the B-net over triangular domain much effectively and conveniently. Based on a new symmetrical algorithm of partial inverse differences, a novel continued fractions interpolation scheme is presented over arbitrary ortho-triples in R2, which is a bivariate osculatory interpolation formula with one-order partial derivatives at all corner points in the ortho-triples. Furthermore, its characterization theorem is presented by three-term recurrence relations. The new scheme is advantageous over the polynomial one with some numerical examples. |
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Keywords: | Ortho-triple Continued fraction interpolation Partial inverse difference B-net Multiple integral |
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