Related papers: Spectral Analysis and Preconditioned Iterative Sol…
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditioner for the iterative solution of linear systems of the…
While preconditioning is a long-standing concept to accelerate iterative methods for linear systems, generalizations to matrix functions are still in their infancy. We go a further step in this direction, introducing polynomial…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
Spectral estimation can be preformed using the so called THREE-like approach. Such method leads to a convex optimization problem whose solution is characterized through its dual problem. In this paper, we show that the dual problem can be…
Multistep matrix splitting iterations serve as preconditioning for Krylov subspace methods for solving singular linear systems. The preconditioner is applied to the generalized minimal residual (GMRES) method and the flexible GMRES (FGMRES)…
We introduce the concept of structured synthesis for Markov decision processes where the structure is induced from finitely many pre-specified options for a system configuration. The resulting synthesis problem is in general a nonlinear…
The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…
High frequency integral equation methodologies display the capability of reproducing single-scattering returns in frequency-independent computational times and employ a Neumann series formulation to handle multiple-scattering effects. This…
Preconditioners are generally essential for fast convergence in the iterative solution of linear systems of equations. However, the computation of a good preconditioner can be expensive. So, while solving a sequence of many linear systems,…
We study the Spectral Analysis for a class of bounded linear operators T = D + F in a non Archimedean Hilbert space E, where D is a diagonal linear operator and where F is a finite rank linear operator. In this study of the Spectral…
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…
This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of new solution…
The present paper gives a review of our recent progress and latest results for novel linear-algebraic algorithms and its application to large-scale quantum material simulations or electronic structure calculations. The algorithms are…
Classical iterative methods for tomographic reconstruction include the class of Algebraic Reconstruction Techniques (ART). Convergence of these stationary linear iterative methods is however notably slow. In this paper we propose the use of…
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…
This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
A new method for analyzing high-dimensional categorical data, Linear Latent Structure (LLS) analysis, is presented. LLS models belong to the family of latent structure models, which are mixture distribution models constrained to satisfy the…
We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data…
In this paper, we present a preconditioned variant of the generalized successive overrelaxation (GSOR) iterative method for solving a broad class of complex symmetric linear systems. We study conditions under which the spectral radius of…