On a dimensional reduction method. I. The optimal selection of basis functions

Authors:
M. Vogelius and I. Babuška

Journal:
Math. Comp. **37** (1981), 31-46

MSC:
Primary 65N99; Secondary 65J10

DOI:
https://doi.org/10.1090/S0025-5718-1981-0616358-0

MathSciNet review:
616358

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Abstract: This paper is the first in a series of three, which analyze an adaptive approximate approach for solving -dimensional boundary value problems by replacing them with systems of equations in *n*-dimensional space. In this approach the unknown functions of 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.

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0616358-0

Article copyright:
© Copyright 1981
American Mathematical Society