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 | References | Similar Articles | Additional Information

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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M. Vogelius, - M. Vogelius and I. Babuška,
*On a dimensional reduction method. I. The optimal selection of basis functions*, Math. Comp.**37**(1981), no. 155, 31–46. MR**616358**, DOI https://doi.org/10.1090/S0025-5718-1981-0616358-0 - M. Vogelius and I. Babuška,
*On a dimensional reduction method. I. The optimal selection of basis functions*, Math. Comp.**37**(1981), no. 155, 31–46. MR**616358**, DOI https://doi.org/10.1090/S0025-5718-1981-0616358-0
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Article copyright:
© Copyright 1981
American Mathematical Society