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The approximation of bivariate functions by sums of univariate ones using the L1-metric

Published online by Cambridge University Press:  20 January 2009

W. A. Light ,
J. H. McCabe ,
G. M. Phillips  and
E. W. Cheney
W. A. Light
Affiliation:
University of Lancaster (WAL)
J. H. McCabe
Affiliation:
University of St. Andrews (JHM, GMP)
G. M. Phillips
Affiliation:
University of St. Andrews (JHM, GMP)
E. W. Cheney
Affiliation:
University of Texas, Austin (EWC)
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We shall study a special case of the following abstract approximation problem: givena normed linear space E and two subspaces, M1 and M2, of E, we seek to approximate f ∈ E by elements in the sum of M1 and M2. In particular, we might ask whether closest points to f from M = M1 + M2 exist, and if so, how they are characterised. If we can define proximity maps p1 and p2 for M1 and M2, respectively, then an algorithm analogous to the one given by Diliberto and Straus [4] can be defined by the formulae

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 25 , Issue 2 , June 1982 , pp. 173 - 181
Copyright
Copyright © Edinburgh Mathematical Society 1982

References

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