This paper is the second in a series of three that analyze a method of dimensional reduction. It contains some results for approximation of functions on the interval [-1, 1] with elements from the null-space of PN, N > 1, where P is a second-order ordinary differential operator. A special case of this is approximation by polynomials. The one-dimensional results are used as a tool to prove similar versions in several dimensions. These multi-dimensional results are directly related to the approximate method of dimensional reduction that was introduced in , and they lead to statements about the convergence properties of this approach. The third paper, which analyzes the adaptive aspects of the method, is forthcoming.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics