Isolating Error Effects in Solving Ill-Posed Problems

Many ill-posed problems are reduced to a matrix equation, usually very ill-conditioned, which is then solved using the smoothing techniques of regularization. Any such smoothing will introduce bias into the calculated solution in the sense that if the data were exact, the calculated solution will no...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 1983-09, Vol.4 (3), p.371
Main Authors: Aulick, C. Mark, Gallie, Thomas M
Format: Article
Language:English
Subjects:
Bias
Computer science
Regularization methods
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Summary:Many ill-posed problems are reduced to a matrix equation, usually very ill-conditioned, which is then solved using the smoothing techniques of regularization. Any such smoothing will introduce bias into the calculated solution in the sense that if the data were exact, the calculated solution will not be the "exact" solution. Since this calculated solution is also affected by error in the data, we show how these two error effects may be isolated and considered separately. Using a very general form of the regularization technique, we derive exact formulas for each error component which illustrates the dependence of each upon the different variables and parameters of the problem.
ISSN:0895-4798
1095-7162
DOI:10.1137/0604037