A New Method of Constructing Bivariate Vector Valued Rational Interpolation Function
Received:October 17, 2009  Revised:January 12, 2011
Key Word: bivariate vector valued rational interpolation   nonnegative integer parameter   divide piece   primary function   interpolation formula.
Fund ProjectL:Supported by Shanghai Natural Science Foundation (Grant No.10ZR1410900), Key Disciplines of Shanghai Municipality (Grant No.S30104), the Anhui Provincial Natural Science Foundation (Grant No.070416227) and Students' Innovation Foundation of Hefei University of Technology (Grant No.XS08079).
 Author Name Affiliation Lin ZHENG Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China Gong Qin ZHU Department of Mathematics, Hefei University of Technology, Anhui 230009, P. R. China
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At present, the methods of constructing vector valued rational interpolation function in rectangular mesh are mainly presented by means of the branched continued fractions. In order to get vector valued rational interpolation function with lower degree and better approximation effect, the paper divides rectangular mesh into pieces by choosing nonnegative integer parameters $d_{1}~(0\leq d_{1}\leq m)$ and $d_{2}~(0\leq d_{2}\leq n)$, builds bivariate polynomial vector interpolation for each piece, then combines with them properly. As compared with previous methods, the new method given by this paper is easy to compute and the degree for the interpolants is lower.