Regularization of linear ill-posed problems involving multiplication operators
نویسندگان
چکیده
منابع مشابه
Ill-Posed and Linear Inverse Problems
In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.
متن کاملFractional Tikhonov regularization for linear discrete ill- posed problems
Tikhonov regularization is one of the most popular methods for solving linear systems of equations or linear least-squares problems with a severely ill-conditioned matrix A. This method replaces the given problem by a penalized least-squares problem. The present paper discusses measuring the residual error (discrepancy) in Tikhonov regularization with a seminorm that uses a fractional power of ...
متن کاملFractional regularization matrices for linear discrete ill-posed problems
The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore t...
متن کاملSquare regularization matrices for large linear discrete ill-posed problems
Large linear discrete ill-posed problems with contaminated data are often solved with the aid of Tikhonov regularization. Commonly used regularization matrices are finite difference approximations of a suitable derivative and are rectangular. This paper discusses the design of square regularization matrices that can be used in iterative methods based on the Arnoldi process for large-scale Tikho...
متن کاملStability Rates for Linear Ill-Posed Problems with Convolution and Multiplication Operators
In this paper we deal with thèstrength' of ill-posedness for ill-posed linear operator equations Ax = y in Hilbert spaces, where we distinguish according to M. Z. Nashed 15] the ill-posedness of type I if A is not compact, but we have R(A) 6 = R(A) for the range R(A) of A; and the ill-posedness of type II for compact operators A: From our considerations it seems to follow that the problems with...
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: Applicable Analysis
سال: 2020
ISSN: 0003-6811,1563-504X
DOI: 10.1080/00036811.2020.1758308