Expansions over a Simplex of Real Functions by Means of Bernoulli Polynomials |
| |
Authors: | F Costabile F Dell'Accio |
| |
Institution: | (1) Università Degli Studi Della Calabria, Italy |
| |
Abstract: | In 1] there is an expansion in Bernoulli polynomials for sufficiently smooth real functions in an interval a,b] R that has useful applications to numerical analysis. An analogous result in a 2-dimensional context is derived in 2] in the case of rectangle. In this note we generalize the above-mentioned one-dimensional expansion to the case of C
m
-functions on a 2-dimensional simplex; a method to generalize the expansion on an N-dimensional simplex is also discussed. This new expansion is applied to find new cubature formulas for 2-dimensional simplex. |
| |
Keywords: | Bernoulli polynomials expansion simplex |
本文献已被 SpringerLink 等数据库收录! |