Polynomial approximation of CM functions by means of boundary values and applications:: A survey

[摘要] We collect classical and more recent results on polynomial approximation of sufficiently regular real functions defined in bounded closed intervals by means of boundary values only. The problem is considered from the point of view of the existence of explicit formulas, interpolation to boundary data, bounds for the remainder and convergence of the polynomial series. Applications to some problems of numerical analysis are pointed out, such as nonlinear equations, numerical differentiation and integration formulas, special associated differential boundary value problems. Some polynomial expansions for smooth enough functions defined in rectangles or in triangles of R-2 as well as in cuboids or in tetrahedrons in R-3 and their applications are also discussed. (C) 2006 Elsevier B.V. All rights reserved.

[发布日期] 2007-12-31

[效力级别]  Proceedings Paper

[关键词] polynomial approximation;boundary value;nonlinear equation;differential boundary value problem;numerical differentiation;numerical integration;multivariate approximation