We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert space, we propose a generalization which involves the iterative solution of simpler subproblems. Descent and convergence properties of this new algorithm are...

The explicit implicit domain decomposition methods are a non iterative types of methods for non overlapping domain decomposition. In comparison with the classical Schwarz algorithm for parabolic problem the former methods are computationally and communicationally more efficient for each time step but due to the use of the explicit step for the interface prediction the methods suffer from the ac...

Results on stability of both local and global metric regularity under set-valued perturbations are presented. As an application, we study (super)linear convergence of a Newtontype iterative process for solving generalized equations. We investigate several iterative schemes such as the inexact Newton’s method, the nonsmooth Newton’s method for semismooth functions, the inexact proximal point alg...

Some matrix-splitting iterative methods for solving systems of linear equations contain parameters that need to be specified in advance, and the choice these directly affects efficiency corresponding methods. This paper uses a Bayesian inference-based Gaussian process regression (GPR) method predict relatively optimal some HSS-type iteration provide extensive numerical experiments compare predi...

We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on m...

We study the convergence of P -regular splitting iterative methods for non-Hermitian positive definite linear systems. Our main result is that P -regular splittings of the form A = M−N , where N = N, are convergent. Natural examples of splittings satisfying the convergence conditions are constructed, and numerical experiments are performed to illustrate the convergence results obtained.

This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based restoration algorithms to account for the observed image being corrupted by mixed Poisson-Gaussian noise and quantization errors.

Abstract: We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractiona...