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Chain least squares method and ill-posed problems | ||
| Iranian Journal of Science | ||
| مقاله 5، دوره 38، شماره 2، مرداد 2014، صفحه 123-132 اصل مقاله (128.47 K) | ||
| نوع مقاله: Regular Paper | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2014.1993 | ||
| نویسندگان | ||
| E. Babolian1؛ A. Abdollahi* 2؛ S. Shahmorad3 | ||
| 1Department of Mathematics, Science and Research Branch, Islamic Azad University, P. O. Box 775-14515, Tehran, Iran | ||
| 2Department of Mathematics, Science and Research Branch, Islamic Azad University, P. O. Box 775-14515, Tehran, Iran | ||
| 3Faculty of Mathematical Science, University of Tabriz, P. O. Box 51664-16471, Tabriz, Iran | ||
| چکیده | ||
| 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 ones, in a way that the condition number of the corresponding system with -dimensional problem will be low. At first, the new method is introduced for and -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. | ||
| کلیدواژهها | ||
| Lagrange multipliers method؛ Chain least squares؛ ill-posed problem؛ Integral equations | ||
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