Related papers: Two-step scale-splitting method for solving comple…
We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…
This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schr\"{o}dinger equations (NLS). The method is explicit, unconditionally stable and time transversal invariant.…
This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…
We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…
The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…
This paper aims to answer an open question recently posed in the literature, that is to find a fast exact method for solving the p-dispersion-sum problem (PDSP), a nonconcave quadratic binary maximization problem. We show that, since the…
In this work we study a multi-step scheme on time-space grids proposed by W. Zhao et al. [28] for solving backward stochastic differential equations, where Lagrange interpolating polynomials are used to approximate the time-integrands with…
In this paper we consider some non-stationary relaxed synchronous and asynchronous multi-splitting methods for solving the linear complementarity problems with their coefficient matrices being H-matrices. The convergence theorems of the…
This is the first in a series of papers which deal with the development of novel methods for solving a system of linear algebraic equations with a time complexity lower than existing algorithms. The NxN system of linear equations, Ax = b,…
We propose a Multi-step Screening Procedure (MSP) for the recovery of sparse linear models in high-dimensional data. This method is based on a repeated small penalty strategy that quickly converges to an estimate within a few iterations.…
We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…
In this paper we examine iterative methods for solving the forward ($A{\bf x}={\bf b}$) and adjoint ($A^{T}{\bf y}={\bf g}$) systems of linear equations used to approximate the scattering amplitude, defined by ${\bf g}^{T}{\bf x}={\bf…
This paper introduces and analyzes a preconditioned modified of the Hermitian and skew-Hermitian splitting (PMHSS). The large sparse continuous Sylvester equations are solved by PMHSS iterative algorithm based on nonHermitian, complex,…
A class of monotone operator equations, which can be decomposed into sum of the gradient of a strongly convex function and a linear and skew-symmetric operator, is considered in this work. Based on discretization of the generalized gradient…
We propose a simple doubly stochastic block Gauss--Seidel algorithm for solving linear systems of equations. By varying the row partition parameter and the column partition parameter of the coefficient matrix, we recover the Landweber…
Tau-leaping is a family of algorithms for the approximate simulation of the discrete state continuous time Markov chains. Motivation for the development of such methods can be found, for instance, in the fields of chemical kinetics and…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
This paper introduces a spectral Monte Carlo iterative method (SMC) for solving linear Poisson and parabolic equations driven by $\alpha$-stable L\'evy process with $\alpha\in (0,2)$, which was initially proposed and developed by Gobet and…