‘Modified Hermitian and skew‐Hermitian splitting methods for non‐Hermitian positive‐definite linear systems’ [Numer. Linear Algebra Appl. 14 (2007) 217–235]

In this note, some errors in the article (Numer. Linear Algebra Appl. 2007; 14 :217–235) are pointed out and some correct results are presented. Copyright © 2011 John Wiley & Sons, Ltd.     

A short note on the paper “Convergence of the TAGE iterative method for the system arisen from the cubic spline approximation for the solution of two-point BVPs with forcing function in integral form”, by Mohanty, Jain and Dhall

In this note, we point out an error in the recently published article [R.K. Mohanty, M.K. Jain, D. Dhall, A cubic spline approximation and application of TAGE iterative method for the solution of two-point boundary value problems with forcing function in integral form, Appl. Math. Model. 35 (2011) 3036-3047] and then correct it.     

Preconditioned GSOR iterative method for a class of complex symmetric system of linear equations

In this paper, we present a preconditioned variant of the generalized successive overrelaxation (GSOR) iterative method for solving a broad class of complex symmetric linear systems. We study conditions under which the spectral radius of the iteration matrix of the preconditioned GSOR method is smaller than that of the GSOR method and determine the optimal values of iteration parameters. Numerical experiments are given to verify the validity of the presented theoretical results and the effectiveness of the preconditioned GSOR method. Copyright © 2015 John Wiley & Sons, Ltd.     

Simulation of turbulent dispersion using Weierstrass modes

A simple fractal model is proposed for the dispersion of passive scalars in an incompressible homogeneous turbulent flow field. The dispersion process is based on a three-dimensional velocity field which is assumed to be a linear superposition of Taylor-Green vortices with wave numbers and amplitudes as those in a Weierstrass function. The chosen velocity field satisfies the continuity equation as well as Kolmogorov's inertial range power law, and has a fractal dimension D between upper and lower length-scale bounds. A cloud of tracer particles is relased into the flow field and dispersed by the fluid motion, the trajectories are numerically integrated from the velocity field. The puffs which result from this process are used to examine some aspects of turbulent dispersion, through comparisons with integrated concentration wind-tunnel measurements. The agreement between numerical and experimental results indicates the significance of the proposed simulation model.     

Generalized Jacobi and Gauss-Seidel Methods for Solving Linear System of Equations

The Jacobi and Gauss-Seidel algorithms are among the stationary iterative methods for solving linear system of equations. They are now mostly used as precondition-ers for the popular iterative solvers. In this paper a generalization of these methods are proposed and their convergence properties are studied. Some numerical experiments are given to show the efficiency of the new methods.     

On the Generalized Deteriorated Positive Semi-Definite and Skew-Hermitian Splitting Preconditioner

For nonsymmetric saddle point problems, Huang et al. in [Numer. Algor. 75 (2017), pp. 1161-1191] established a generalized variant of the deteriorated positive semi-definite and skew-Hermitian splitting (GVDPSS) preconditioner to expedite the convergence speed of the Krylov subspace iteration methods like the GMRES method. In this paper, some new convergence properties as well as some new numerical results are presented to validate the theoretical results.     

A New Iteration and Preconditioning Method for Elliptic PDE-Constrained Optimization Problems

Optimal control problems constrained by a partial differential equation (PDE) arise in various important applications, such as in engineering and natural sciences. Normally the problems are of very large scale, so iterative solution methods must be used. Thereby the choice of an iteration method in conjunction with an efficient preconditioner is essential. In this paper, we consider a new iteration method and a new preconditioning technique for an elliptic PDE-constrained optimal control problem with a distributed control function. Some earlier used iteration methods and preconditioners in the literature are compared, both analytically and numerically with the new iteration method and the preconditioner.