On Minimal Positive and Self-Contained Multi-Dimensional Integration Formulas

摘要

An approximate integration formula for a region R in n-dimensional Euclidean space E sub n, with nodes x sub k and weights A sub k, is said to be of degree m if it is exact for all polynomials of degree at most m in the n variables. For low degree (O is less than or equal to m is less than or equal to 3), this thesis is concerned with the determination of the minimal number N of nodes for which there exists a formula of degree m which is positive or self-contained for all R is an element of R, some 'reasonable' class of measurable subsets of E sub n. (Author)