Inverse Toeplitz preconditioners for ill-posed problems
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 کاملInverse Toeplitz preconditioners for Hermitian Toeplitz systems
In this paper we consider solving Hermitian Toeplitz systems Tnx= b by using the preconditioned conjugate gradient (PCG) method. Here the Toeplitz matrices Tn are assumed to be generated by a non-negative continuous 2 -periodic function f, i.e. Tn =Tn[f]. It was proved in (Linear Algebra Appl. 1993; 190:181) that if f is positive then the spectrum of Tn[1=f]Tn[f] is clustered around 1. We prove...
متن کاملHybrid Samplers for Ill-Posed Inverse Problems
In the Bayesian approach to ill-posed inverse problems, regularization is imposed by specifying a prior distribution on the parameters of interest and Markov chain Monte Carlo samplers are used to extract information about its posterior distribution. The aim of this paper is to investigate the convergence properties of the random-scan random-walk Metropolis (RSM) algorithm for posterior distrib...
متن کاملOptimal order multilevel preconditioners for regularized ill-posed problems
In this article we design and analyze multilevel preconditioners for linear systems arising from regularized inverse problems. Using a scaleindependent distance function that measures spectral equivalence of operators, it is shown that these preconditioners approximate the inverse of the operator to optimal order with respect to the spatial discretization parameter h. As a consequence, the numb...
متن کاملCauchy-like Preconditioners for Two-Dimensional Ill-Posed Problems
Ill-conditioned matrices with block Toeplitz, Toeplitz block (BTTB) structure arise from the discretization of certain ill-posed problems in signal and image processing. We use a preconditioned conjugate gradient algorithm to compute a regularized solution to this linear system given noisy data. Our preconditioner is a Cauchy-like block diagonal approximation to an orthogonal transformation of ...
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: Linear Algebra and its Applications
سال: 1998
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(98)10046-0