Piecewise Polynomial Functions

摘要

This report contains a series of talks presented during the summer of 1975 at LLL on the general topic of piecewise polynomial functions. Such functions offer simple, accurate, economical, and flexible procedures for solving a wide variety of problems. The emphasis is on curve fitting, surface fitting, and applications to finite element approximations. This discussion is not intended as an all-inclusive, general presentation of piecewise polynomials. Rather, attention is directed to the basic of cubic (and bicubic) interpolation and approximation, since they represent a good first choice for many problems when increased accuracy over linear (or bilinear) approximations is desired. The text is divided into sections on univariate functions, cubic splines, bivariate functions, blending functions, and nonrectangular domains. 10 figures, 1 table. (ERA citation 01:015378)