General Order Newton-Pad6 Approximants for Multivariate Functions
نویسندگان
چکیده
Pad6 approximants are a frequently used tool for the solution of mathematical problems. One of the main drawbacks of their use for multivariate functions is the calculation of the derivatives of f ( x 1 .... ,xp). Therefore multivariate Newton-Pad6 approximants are introduced; their computation will only use the value of f at some points. In Sect. 1 we shall repeat the univariate Newton-Pad6 approximation problem which is a rational Hermite interpolation problem. In Sect. 2 we sketch some problems that can arise when dealing with multivariate interpolation. In Sect. 3 we define multivariate divided differences and prove some lemmas that will be useful tools for the introduction of multivariate Newton-Pad6 approximants in Sect. 4. A numerical example is given in Sect. 5, together with the proof that for p = l the classical Newton-Pad6 approximants for a univariate function are obtained.
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