Book Review: Linear operators and 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 کاملIll-posed problems with unbounded operators
Let A be a linear, closed, densely defined unbounded operator in a Hilbert space. Assume that A is not boundedly invertible. If Eq. (1) Au = f is solvable, and ‖fδ − f ‖ δ, then the following results are provided: Problem Fδ(u) := ‖Au− fδ‖2 + α‖u‖2 has a unique global minimizer uα,δ for any fδ , uα,δ = A∗(AA∗ + αI)−1fδ . There is a function α = α(δ), limδ→0 α(δ)= 0 such that limδ→0 ‖uα(δ),δ − y...
متن کاملLinear ill - posed problems and dynamical systems ∗ †
A new approach to solving linear ill-posed problems is proposed. The approach consists of solving a Cauchy problem for a linear operator equation and proving that this problem has a global solution whose limit at infinity solves the original linear equation.
متن کاملFGMRES for linear discrete ill-posed problems
GMRES is one of the most popular iterative methods for the solution of large linear systems of equations. However, GMRES generally does not perform well when applied to the solution of linear systems of equations that arise from the discretization of linear ill-posed problems with error-contaminated data represented by the right-hand side. Such linear systems are commonly referred to as linear ...
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...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1997
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-97-00709-x