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Mathematics of Computation

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On the convergence of an algorithm computing minimum-norm solutions of ill-posed problems

Author: J. T. Marti
Journal: Math. Comp. 34 (1980), 521-527
MSC: Primary 65J10; Secondary 47A50
MathSciNet review: 559200
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Abstract: The paper studies a finite element algorithm giving approximations to the minimum-norm solution of ill-posed problems of the form $Af = g$, 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 $A{A^\ast }$. 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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Keywords: Ill-posed problem, algorithm, minimum-norm solution, Fredholm integral equation of the first kind
Article copyright: © Copyright 1980 American Mathematical Society