相关论文: Preconditioning rectangular spectral collocation

In this work, we propose a novel preconditioned Krylov subspace method for solving an optimal control problem of wave equations, after explicitly identifying the asymptotic spectral distribution of the involved sequence of linear…

Wideband communication receivers often deal with the problems of detecting weak signals from distant sources received together with strong nearby interferers. When the techniques of random modulation are used in communication system…

Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear…

We present a novel approach to reverse Monte Carlo (RMC) modeling, SpecSwap-RMC, which makes use of pre-computed property data from a discrete configuration space replacing atomistic moves with swap moves of contributions to a sample-set…

We shall propose and analyze some new preconditioners for the saddle-point systems arising from the edge element discretization of the time-harmonic Maxwell equations in three dimensions. We will first consider the saddle-point systems with…

Coupled systems of free flow and porous media arise in a variety of technical and environmental applications. For laminar flow regimes, such systems are described by the Stokes equations in the free-flow region and Darcy's law in the porous…

This work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science. Here we propose a new technique to force the positive…

We describe a randomized Krylov-subspace method for estimating the spectral condition number of a real matrix A or indicating that it is numerically rank deficient. The main difficulty in estimating the condition number is the estimation of…

In this paper we present a pseudospectral method in the disk. Unlike the methods known until now, the disk is not duplicated. Moreover, we solve the Laplace equation subjected to nonhomogeneous Dirichlet, Neumann and Robin boundary…

A class of preconditioners is introduced to enhance geometry optimisation and transition state search of molecular systems. We start from the Hessian of molecular mechanical terms, decompose it and retain only its positive definite part to…

In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the…

We investigate the spectrum of differentiation matrices for certain operators on the sphere that are generated from collocation at a set of scattered points $X$ with positive definite and conditionally positive definite kernels. We focus on…

We have presented a fast method for solving a specific type of block four-by-four saddlepoint problem arising from the finite element discretization of the generalized 3D Stokes problem. We analyze the eigenvalue distribution and the…

We present applications of rectangular matrix models to various combinatorial problems, among which the enumeration of face-bicolored graphs with prescribed vertex degrees, and vertex-tricolored triangulations. We also mention possible…

This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…

Spectral and spectral element methods using Galerkin type formulations are efficient for solving linear fractional PDEs (FPDEs) of constant order but are not efficient in solving nonlinear FPDEs and cannot handle FPDEs with variable-order.…

In this article we construct and analyze multigrid preconditioners for discretizations of operators of the form D+K* K, where D is the multiplication with a relatively smooth positive function and K is a compact linear operator. These…

We present a novel numerical solver for the systems of coupled non-linear elliptical differential equations. The solver partitions the computational domain into a set of rectangular pseudo-spectral collocation subdomains and is especially…

The conditioning of implicit Runge-Kutta (RK) integration for linear finite element approximation of diffusion equations on general anisotropic meshes is investigated. Bounds are established for the condition number of the resulting linear…

In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…