Abstract
A new conjugate gradient method is proposed for solving the linear ill-posed problem and the application to the identification of the multi-source dynamic loads on a surface of simply supported plate. The algorithm considered here is detailedly given and proved that the computational costs for the present method are nearly the same as the common conjugate gradient method, but the number of iteration steps is even less. Finally, the performances of numerical simulations are given, and verify the favorable theoretical properties of the present method.
Highlights
Many works have been done for regularization of linear ill-posed problems [1,2,3,4,5]
We will investigate the convergence behavior of Algorithm 2.1 under the following two assumptions, which are often used in the literature to study the global convergence of conjugate gradient methods with inexact line search
A new conjugate gradient method is presented and considered as an alternative to approximate the true solution of the illposed problem of Fredholm integral equations of the first kind
Summary
Many works have been done for regularization of linear ill-posed problems [1,2,3,4,5]. An augmented Galerkin method was suggested to solve the first kind Fredholm integral equations problem which is often ill-posed [10]. For solving the first kind Fredholm integral equations problem by the conjugate gradient method, as we know, very few papers can be found and very limited. These inverse problems mentioned by most of papers above are ill-posed. >0 holds due to the line search condition (2.6), so the formula (2.8) is validly defined It means that this formula (2.8) correspondingly generates a conjugate gradient method.
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