On the convergence of an algorithm computing minimumnorm solutions of illposed problems
Author:
J. T. Marti
Journal:
Math. Comp. 34 (1980), 521527
MSC:
Primary 65J10; Secondary 47A50
MathSciNet review:
559200
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Abstract: The paper studies a finite element algorithm giving approximations to the minimumnorm solution of illposed problems of the form , where A is a bounded linear operator from one Hubert space to another. It is shown that the algorithm is norm convergent in the general case and an error bound is derived for the case where g is in the range of . As an example, the method has been applied to the problem of evaluating the second derivative f of a function g numerically.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198005592008
PII:
S 00255718(1980)05592008
Keywords:
Illposed problem,
algorithm,
minimumnorm solution,
Fredholm integral equation of the first kind
Article copyright:
© Copyright 1980
American Mathematical Society
