Open AccessBook
An Introduction to Iterative Toeplitz Solvers
Raymond H. Chan,Xiao-Qing Jin +1 more
Reads0
Chats0
TLDR
The present work presents a unified treatment from kernels system for block Toeplitz systems and some examples of such systems have been described in detail in the literature.Abstract:
Preface 1. Introduction 2. Circulant preconditioners 3. Unified treatment from kernels 4. Ill-conditioned Toeplitz systems 5. Block Toeplitz systems A. M-files used in the book Bibliography.read more
Citations
More filters
Journal ArticleDOI
A class of second order difference approximations for solving space fractional diffusion equations
TL;DR: A class of second order approximations, called the weighted and shifted Grunwald difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional diffusion equations in one and two dimensions.
Journal ArticleDOI
Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
Zhibo Wang,Seakweng Vong +1 more
TL;DR: In this paper, compact finite difference schemes for the modified anomalous fractional sub-diffusion equation and fractional diffusion-wave equation are studied, and based on the idea of weighted and shifted Grunwald difference operator, they establish schemes with temporal and spatial accuracy order equal to two and four respectively.
Journal ArticleDOI
A circulant preconditioner for fractional diffusion equations
Siu-Long Lei,Hai-Wei Sun +1 more
TL;DR: The implicit finite difference scheme with the shifted Grunwald formula is employed to discretize fractional diffusion equations and the spectrum of the preconditioned matrix is proven to be clustered around 1 if diffusion coefficients are constant; hence the convergence rate of the proposed iterative algorithm is superlinear.
Journal ArticleDOI
Mode Division Multiplexing Communication Using Microwave Orbital Angular Momentum: An Experimental Study
TL;DR: The system model based on OAM-MDM is mathematically analyzed and it is theoretically concluded that such system architecture can bring a vast reduction in receiver complexity without capacity penalty compared with conventional line-of-sight multiple-in-multiple-out systems under the same physical constraint.
Journal ArticleDOI
Multigrid method for fractional diffusion equations
Hong-Kui Pang,Hai-Wei Sun +1 more
TL;DR: The fractional diffusion equation is discretized by the implicit finite difference scheme with the shifted Grunwald formula and the coefficient matrix possesses the Toeplitz-like structure and a multigrid method is proposed to solve the resulting system.