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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 $ (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.


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DOI: https://doi.org/10.1090/S0025-5718-1981-0616358-0
Article copyright: © Copyright 1981 American Mathematical Society