Remarks on the convergence of an iterative method of solution of generalized least squares problem

• Autorzy: Bartoszewski Z.
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider an iterative method of finding a regularized solution of a general linear system Ax = b. For a given scalar α and an initial vector g it produces a sequence that converges to the least squares solution of this system. The limiting point minimizes the distance between g and the set of all least squares solutions of the problem. An estimate of the rate of convergence is also provided.

Słowa kluczowe

EN

iterative methods; generalized inverse matrices; least squares problem; regularization of ill-posed problems

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2010
• Tom: Vol. 43, nr 4
• Strony: 931--938
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Bartoszewski Z.

• The Faculty of Applied Physics and Mathematics Gdańsk University Of Technology ul. G. Narutowicza 11/12 80-233 Gdańsk, Poland,

Bibliografia

• [1] Z. Bartoszewski, A correction and discretization of the general linear boundary value problem for nonlinear systems of ordinary differential equations in normal form, Ph. D. Thesis, Lomonosov University, Moscow, 1982 (in Russian).
• [2] Å. Björk, Numerical Methods for Least Squers Problems, SIAM, Philadelphia, 1996.
• [3] G. H. Golub, C. F. Van Loan, Matrix Computations, The John Hopkins University Press, Baltimore, 1989.
• [4] A. D. Gorbunov, Methods of Solving of Nonlinear Problems, Lomonosov University, Moscow, 1980 (in Russian).
• [5] V. A. Morozov, Regularization Methods for Ill-posed Problems, CRC Press, Boca Raton, FL, 1993.
• [6] V. A. Morozov, On the rate of convergence for regularized solutions, Numer. Funct. Anal. Optim. 19, 3-4 (1998), 345–352.