When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

In this expository paper, we survey some of the latest developments in using preconditioned
conjugate gradient methods for solving Toeplitz systems. One of the main results is that the …

Page 1 NUMERICAL MATHEMATICS AND SCIENTIFIC COMPUTATION Iterative Methods
for Toeplitz Systems MICHAEL K. NG OXFORD SCIENCE PUBLICATIONS Page 2 Page 3 …

Fractional partial order diffusion equations are a generalization of classical partial
differential equations, used to model anomalous diffusion phenomena. When using the …

The fractional diffusion equation is discretized by the implicit finite difference scheme with
the shifted Grünwald formula. The scheme is unconditionally stable and the coefficient …

We consider fast solvers for large linear systems arising from the Galerkin approximation
based on B-splines of classical d-dimensional elliptic problems, d≥ 1, in the context of …

We are concerned with the behavior of the minimum (maximum) eigenvalue λ0 (n)(λn (n)) of
an (n+ 1)×(n+ 1) Hermitian Toeplitz matrix Tn (ƒ) where ƒ is an integrable real-valued …

Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced
as a generalization both of classical Toeplitz sequences and of variable coefficient …

In this paper, we analyze the spectra of the preconditioned matrices arising from discretized
multi-dimensional Riesz spatial fractional diffusion equations. The finite difference method is …

We consider a boundary value problem in weak form of a steady-state Riesz space-
fractional diffusion equation (FDE) of order 2-α with 0<α<1. By using a finite volume …