Optimal-order convergence of Nesterov acceleration for linear ill-posed problems*
نویسندگان
چکیده
We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided a parameter chosen accordingly to the smoothness of solution. This result proven both priori stopping rule and discrepancy principle. The essential tool obtain this representation residual polynomials via Gegenbauer polynomials.
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 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 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 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 کاملOptimal Regularization for Ill-Posed Problems in Metric Spaces
We present a strategy for choosing the regularization parameter (Lepskij-type balancing principle) for ill-posed problems in metric spaces with deterministic or stochastic noise. Additionally we improve the strategy in comparison to the previously used version for Hilbert spaces in some ways. AMS-Classification: 47A52, 65J22, 49J35, 93E25
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: Inverse Problems
سال: 2021
ISSN: ['0266-5611', '1361-6420']
DOI: https://doi.org/10.1088/1361-6420/abf5bc