TITLE

A randomized method for solving discrete ill-posed problems

AUTHOR(S)
Rachkovskij, D.; Revunova, E.
PUB. DATE
July 2012
SOURCE
Cybernetics & Systems Analysis;Jul2012, Vol. 48 Issue 4, p621
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
An approach is proposed to the stable solution of discrete ill-posed problems on the basis of a combination of random projection of the initial ill-conditioned matrix with an ill-defined numerical rank and the pseudo-inversion of the resultant matrix. To select the dimension of the projection matrix, we propose to use criteria for the selection of a model and a regularization parameter. The results of experimental studies based on the well-known examples of discrete ill-posed problems are presented. Their solution errors are close to the Tikhonov regularization error, but a matrix dimension reduction owing to projection reduces the expenditures for computations, especially at high noise levels.
ACCESSION #
79824079

 

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