On a Dimensional Reduction Method. The Optimal Selection of Basis Functions

摘要

This paper is the first in a series of three, which analyze an adaptive approximate approach for solving (n+1)- dimensional boundary value problems by replacing them with systems of equations in n-dimensional space. In this approach the unknown functions of (n+1)- variables are projected onto finite linear combinations of functions of just n-variables. This paper shows how the coefficients of these linear combinations can be chosen optimally. (Author)