A best approximation evaluation of a finite element calculation

We discuss an electrostatics problem whose solution must lie in the set S of all real n-by-n symmetric matrices with all row sums equal to zero. With respect to the Frobenius norm, we provide an algorithm that finds the member of S which is closest to any given n-by-n matrix, and determines the dist...

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Bibliographic Details
Published in:Linear algebra and its applications 1999-12, Vol.302-303, p.367-375
Main Authors: Robinson, Allen C., Robinson, Donald W.
Format: Article
Language:English
Subjects:
Best approximation
Computational quality
Matrix inversion
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Summary:We discuss an electrostatics problem whose solution must lie in the set S of all real n-by-n symmetric matrices with all row sums equal to zero. With respect to the Frobenius norm, we provide an algorithm that finds the member of S which is closest to any given n-by-n matrix, and determines the distance between the two. This algorithm makes it practical to find the distances to S of finite element approximate solutions of the electrostatics problem, and to reject those which are not sufficiently close.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(99)00175-5