Related papers: Accelerated Landweber methods based on co-dilated …
This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…
Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…
We study the convergence of the gradient descent method for solving ill-posed problems where the solution is characterized as a global minimum of a differentiable functional in a Hilbert space. The classical least-squares functional for…
Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing…
We present an auxiliary space theory that provides a unified framework for analyzing various iterative methods for solving linear systems that may be semidefinite. By interpreting a given iterative method for the original system as an…
We discuss a fast approximate solution to the associated classical -- classical orthogonal polynomial connection problem. We first show that associated classical orthogonal polynomials are solutions to a fourth-order quadratic eigenvalue…
This paper develops a new class of nonlinear acceleration algorithms based on extending conjugate residual-type procedures from linear to nonlinear equations. The main algorithm has strong similarities with Anderson acceleration as well as…
In this study, we present and analyze a novel variant of the stochastic gradient descent method, referred as Stochastic data-driven Bouligand Landweber iteration tailored for addressing the system of non-smooth ill-posed inverse problems.…
With the development of machine learning and Big Data, the concepts of linear and non-linear optimization techniques are becoming increasingly valuable for many quantitative disciplines. Problems of that nature are typically solved using…
Inexact Newton regularization methods have been proposed by Hanke and Rieder for solving nonlinear ill-posed inverse problems. Every such a method consists of two components: an outer Newton iteration and an inner scheme providing…
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the…
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
We present a family of distributed forward-backward methods with variable stepsizes to find a solution of structured monotone inclusion problems. The framework is constructed by means of relocated fixed-point iterations, extending the…
We revisit a unified methodology for the iterative solution of nonlinear equations in Hilbert spaces. Our key observation is that the general approach from [Heid & Wihler, Math. Comp. 89 (2020), Calcolo 57 (2020)] satisfies an energy…
In the context of linear inverse problems, we propose and study a general iterative regularization method allowing to consider large classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
Combined optimization problems that couple data-fidelity and regularization terms arise naturally in a wide range of inverse problems. In this paper, we study an adaptive randomized averaging block extended Bregman-Kaczmarz (aRABEBK) method…
For a linear complementarity problem, we present a relaxaiton accelerated two-sweep matrix splitting iteration method. The convergence analysis illustrates that the proposed method converges to the exact solution of the linear…
In this work we discuss the possibility to reduce the computational complexity of modal methods, i.e. methods based on eigenmodes expansion, from the third power to the second power of the number of eigenmodes. The proposed approach is…
An iterative scheme for solving ill-posed nonlinear operator equations with monotone operators is introduced and studied in this paper. A Dynamical Systems Method (DSM) algorithm for stable solution of ill-posed operator equations with…