Given m ≥ 1, let Pm(R 2 ) denote the space of all real-valued polynomials in two variables with degree at most m. Let {xi} n i=1 be n distinct points in R2 and s...Gasca, M., and Sauer, T. Polynomial interpolation in several variables. Advances Comput. Math. 12 (2000), ...
(2000b) Polynomial interpolation in several variables. Multivariate polynomial interpolation. Advances in Computational Mathematics 12: 377–410 MATH MathSciNetGasca, M., Sauer, T.: Polynomial interpolation in several variables, in Multivariate polynomial interpolation. Adv. Comput. Math. 12(4), ...
Chebyshev polynomialscrop up in many areas of calculus, includingnumerical integration,orthogonal polynomialsand spectral methods for partialdifferential equations. They can also be used for curve fitting (finding afunctionthat models a curve),interpolationand in multiple other areas ofnumerical analysis. T...
Polynomial Interpolation in Several Variables: Lattices, Differences, and Ideals When passing from one to several variables, the nature and structure of polynomial interpolation changes completely: the solvability of the interpolation problem with respect to a given finite dimensional polynomial space, like...
Polynomial interpolation in several variables, cubature formulae, and ideals[*]Supported by the National Science Foundation under Grant DMS-9802265 In this paper a new approach is outlined to construct cubature formulae for two-dimensional integrals. The method which will be presented is based on a...
Xu, Orthogonal Polynomials of Several Variables, Encyclopedia of Mathematics and its Applications, Cambridge University Press, second ed., 2014. S. Elhay, G. H. Golub, and J. Kautsky, Jacobi matrices for sums of weight functions, BIT, 32 (1992), pp. 143–166. Article MathSciNet Google ...
Although polynomials have several attractive features, polynomial interpolation of a given function often has the drawback of producing approximations that may be wildly oscillatory. To overcome this difficulty we divide the interval of interest into small subintervals and in each subinterval consider polyn...
Polynomial interpolation in several variables This is a survey of the main results on multivariate polynomial interpolation in the last twenty-five years, a period of time when the subject experienced ... M Gasca,T Sauer - 《Advances in Computational Mathematics》 被引量: 609发表: 2000年 ...
of the polynomial when supplied with values for the variables. In Kaltofen and Trager (1988) it is shown that this representation is applicable to several problems such as multivariate polynomial factorization. Clearly, the process of converting a polynomial given by a black box back to the repres...
The coordinates of variables of types III through V can be obtained via 1D, 2D or 3D polynomial interpolation of the nodal data. In this work in particular, we consider one- and two-dimensional domains; the results for these types of variables are given in Section 3. The goal is to ...