11 خرداد 1403
سعيد كريمي جعفر بيگلو

سعید کریمی جعفر بیگلو

مرتبه علمی: دانشیار
نشانی: دانشکده مهندسی سیستم های هوشمند و علوم داده - گروه ریاضی
تحصیلات: دکترای تخصصی / ریاضی
تلفن: 07733447965
دانشکده: دانشکده مهندسی سیستم های هوشمند و علوم داده

مشخصات پژوهش

عنوان DIRECT IMPLEMENTATION OF TIKHONOV REGULARIZATION FOR THE FIRST KIND INTEGRAL EQUATION
نوع پژوهش مقالات در نشریات
کلیدواژه‌ها
First kind integral equation, Golub-Kahan bidiagonalization, Tikhonov regularization, Quadrature Discretization
مجله JOURNAL OF COMPUTATIONAL MATHEMATICS
شناسه DOI doi:10.4208/jcm.2010-m2020-0132
پژوهشگران میثم جوزی (نفر اول) ، سعید کریمی جعفر بیگلو (نفر دوم)

چکیده

A common way to handle the Tikhonov regularization method for the first kind Fredholm integral equations, is first to discretize and then to work with the final linear system. This unavoidably inflicts discretization errors which may lead to disastrous results, especially when a quadrature rule is used. We propose to regularize directly the integral equation resulting in a continuous Tikhonov problem. The Tikhonov problem is reduced to a simple least squares problem by applying the Golub-Kahan bidiagonalization (GKB) directly to the integral operator. The regularization parameter and the iteration index are determined by the discrepancy principle approach. Moreover, we study the discrete version of the proposed method resulted from numerical evaluating the needed integrals. Focusing on the nodal values of the solution results in a weighted version of GKB-Tikhonov method for linear systems arisen from the Nystr¨om discretization. Finally, we use numerical experiments on a few test problems to illustrate the performance of our algorithms.