Related papers: Positive semidefinite/positive semidefinite splitt…
Motivated by the theory of self-duality which provides a variational formulation and resolution for non self-adjoint partial differential equations \cite{G1, G2}, we propose new templates for solving large non-symmetric linear systems. The…
To precondition a large and sparse linear system, two direct methods for approximate factoring of the inverse are devised. The algorithms are fully parallelizable and appear to be more robust than the iterative methods suggested for the…
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…
An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a…
We propose a new approximate factorization for solving linear systems with symmetric positive definite sparse matrices. In a nutshell the algorithm is to apply hierarchically block Gaussian elimination and additionally compress the fill-in.…
Despite hundreds of papers on preconditioned linear systems of equations, there remains a significant lack of comprehensive performance benchmarks comparing various preconditioners for solving symmetric positive definite (SPD) systems. In…
A new domain decomposition preconditioner is introduced for efficiently solving linear systems Ax = b with a symmetric positive definite matrix A. The particularity of the new preconditioner is that it is not necessary to have access to the…
Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
In this paper, we derive a practical, general framework for creating adaptive iterative (linearization or splitting) algorithms to solve multi-physics problems. This means that, given an iterative method, we derive \textit{a posteriori}…
We introduce a new system of split variational inequality problems which is a natural extension of split variational inequality problem in semi-inner product spaces. We use the retraction technique to propose an iterative algorithm for…
In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…
We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…
This article presents a class of modified new modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). By using two positive diagonal matrices, we formulate a fixed-point equation which is…
Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…
The following document presents a possible solution and a brief stability analysis for a nonlinear system, which is obtained by studying the possibility of building a hybrid solar receiver; It is necessary to mention that the solution of…
Positive semidefinite Hermitian matrices that are not fully specified can be completed provided their underlying graph is chordal. If the matrix is positive definite the completion can be uniquely characterized as the matrix that maximizes…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
In this article we present several necessary and sufficient conditions for the existence of Hermitian positive definite solutions of nonlinear matrix equations of the form $X^s + A^*X^{-t}A + B^*X^{-p}B = Q$, where $ s, t, p \geq 1$, $ A,…
In this paper, we propose a preconditioner based on the shift-splitting method for generalized saddle point problems with nonsymmetric positive definite (1,1)-block and symmetric positive semidefinite $(2,2)$-block. The proposed…