Discrepancy Sets for Combined Least Squares Projection and Tikhonov Regularization. Issue 2 (4th March 2017)

• Record Type: Journal Article
• Authors: Regińska, Teresa
• Is Part Of: Mathematical modelling and analysis. Volume 22:Issue 2(2017)
• Page Start: 202
• Page End: 212
• Publication Date: 2017-03-04
• Subjects: linear ill-posed problem -- discrepancy principle -- LSQ projection -- Tikhonov regularization; 65J20 -- 47A52 -- 65F22; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2017.1289987
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: To solve a linear ill-posed problem, a combination of the finite dimensional least squares projection method and the Tikhonov regularization is considered. The dimension of the projection is treated as the second parameter of regularization. A two-parameter discrepancy principle defines a discrepancy set for any data error bound. The aim of the paper is to describe this set and to indicate its subset such that for regularization parameters from this subset the related regularized solution has the same order of accuracy as the Tikhonov regularization with the standard discrepancy principle but without any discretization.