ISSN:
1573-2894
Keywords:
minimal cardinality
;
least norm approximation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract A theoretically justifiable fast finite successive linear approximation algorithm is proposed for obtaining a parsimonious solutionto a corrupted linear system Ax=b+p, where the corruption p is due to noise or error in measurement. The proposedlinear-programming-based algorithm finds a solution x by parametrically minimizing the number of nonzeroelements in x and the error ‖Ax-b-p‖1.Numerical tests on a signal-processing-based exampleindicate that the proposed method is comparable to a method that parametrically minimizesthe 1-norm of the solution x and the error ‖Ax-b-p‖1, and that both methods are superior, byorders of magnitude, to solutions obtained by least squares as well by combinatorially choosing an optimal solution with a specific number of nonzero elements.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018361916442
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