On regularizing effects of MINRES and MR-II for large scale symmetric discrete ill-posed problems
نویسندگان
چکیده
منابع مشابه
On regularizing effects of MINRES and MR-II for large scale symmetric discrete ill-posed problems
Abstract. For large-scale symmetric discrete ill-posed problems, MINRES and MR-II are commonly used iterative solvers. In this paper, we analyze their regularizing effects. We first prove that the regularized solutions by MINRES have filtered SVD forms. Then we show that (i) a hybrid MINRES that uses explicit regularization within projected problems is generally needed to compute a best possibl...
متن کاملProjected Tikhonov Regularization of Large-Scale Discrete Ill-Posed Problems
The solution of linear discrete ill-posed problems is very sensitive to perturbations in the data. Confidence intervals for solution coordinates provide insight into the sensitivity. This paper presents an efficient method for computing confidence intervals for large-scale linear discrete ill-posed problems. The method is based on approximating the matrix in these problems by a partial singular...
متن کاملRegularizing Newton-Kaczmarz Methods for Nonlinear Ill-Posed Problems
We introduce a class of stabilizing Newton-Kaczmarz methods for nonlinear ill-posed problems and analyze their convergence and regularization behaviour. As usual for iterative methods for solving nonlinear ill-posed problems, conditions on the nonlinearity (or the derivatives) have to be imposed in order to obtain convergence. As we shall discuss in general and in some specific examples, the no...
متن کاملThe residual method for regularizing ill-posed problems
Although the residual method, or constrained regularization, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov regularization, where a series of new results for regularization in Banach spaces has been published in the recent years. The present paper intends to bridge the gap between the existin...
متن کاملIterative Solution Methods for Large Linear Discrete Ill-posed Problems
This paper discusses iterative methods for the solution of very large severely ill-conditioned linear systems of equations that arise from the discretization of linear ill-posed problems. The right-hand side vector represents the given data and is assumed to be contaminated by errors. Solution methods proposed in the literature employ some form of ltering to reduce the in uence of the error in ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2017
ISSN: 0377-0427
DOI: 10.1016/j.cam.2017.02.008