For a sparse symmetric matrix, there has been much attention given to algorithms for reducing the bandwidth. As far as we can see, little has been done for the unsymmetric matrix A, which has distinct lower and upper bandwidths l and u. When Gaussian elmination with row interchanges is applied, the lower bandwidth is unaltered while the upper bandwidth becomes l+u. With column interchanges, the...

GMRES is a popular iterative method for the solution of linear system of equations with an unsymmetric square matrix. Range restricted GMRES (RRGMRES) is one GMRES version proposed by Calvetti et al in 2000. In this paper, a weighted implementation for RRGMRES is proposed. Numerical results prove this weighted RRGMRES is better than RRGMRES.

Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed at each iteration step by a suitable approximation process, e.g., by GMRES itself.

Solving partial diierential equations by collocation with radial basis functions can be eeciently done by a technique rst proposed by E. Kansa in 1990. It rewrites the problem as a generalized interpolation problem, and the solution is obtained by solving a (possibly large) linear system. The method has been used successfully in a variety of applications, but a proof of nonsingularity of the li...

We introduce an iterative method named Gpmr (general partitioned minimum residual) for solving block unsymmetric linear systems. is based on a new process that simultaneously reduces two rectangular matrices to upper Hessenberg form and closely related the block-Arnoldi process. tantamount Block-Gmres with right-hand sides in which approximate solutions are summed at each iteration, but its sto...

Second order methods for optimization call for the solution of sequences of linear systems. In this survey we will discuss several issues related to the preconditioning of such sequences. Covered topics include both techniques for building updates of factorized preconditioners and quasi-Newton approaches. Sequences of unsymmetric linear systems arising in NewtonKrylov methods will be considered...

It is well known that the solution of sparse linear systems, generally expressed in the form Ax = b, is a core task of numerical simulation. In case of semiconductor device simulation the coefficient matrix A is unsymmetric, but structurally symmetric ([2]). The solution of linear systems can be achieved by iterative or direct methods. While iterative methods do not always lead to a solution du...