Author/Authors :
Babolian، E نويسنده Department of Mathematics, Science and Research Branch, Islamic Azad University, P. O. Box 775-14515, Tehran, Iran Babolian, E , Abdollahi، A نويسنده 1Department of Mathematics, Science and Research Branch, Islamic Azad University, P. O. Box 775-14515, Tehran, Iran Abdollahi, A , Shahmorad، S نويسنده Faculty of Mathematical Science, University of Tabriz, P. O. Box 51664-16471, Tabriz, Iran Shahmorad, S
Abstract :
The main purpose of this article is to increase the efficiency of the least squares method in numerical solution of
ill-posed functional and physical equations. Determining the least squares of a given function in an arbitrary set is
often an ill-posed problem. In this article, by defining artificial constraint and using Lagrange multipliers method,
the attempt is to turn ??-dimensional least squares problems into ???? ?? 1?? ones, in a way that the condition number
of the corresponding system with ???? ?? 1??-dimensional problem will be low. At first, the new method is introduced
for 2 and 3-term basis, then the presented method is generalized for ??-term basis. Finally, the numerical solution
of some ill-posed problems like Fredholm integral equations of the first kind and singularly perturbed linear
Fredholm integral equations of the second kind are approximated by chain least squares method. Numerical
comparisons indicate that the chain least squares method yields accurate and stable approximations in many cases.
