Adaptive version of Simpler GMRES

A New Version for Simpler GMRES

GMRES is an iterative method that provides better solutions when dealing with larg linear systems of equations with unsymmetric coefficient matrix. By shifting the Arnoldi process to begin with Ar0 instead of r0, simpler GMRES implementation, proposed by Walker and Zhou in 1994, is obtained that in this method, an upper triangular problem is solved instead of hessenberg least square problem. Th...

How to Make Simpler GMRES and GCR More Stable

In this paper we analyze the numerical behavior of several minimum residual methods, which are mathematically equivalent to the GMRES method. Two main approaches are compared: the one that computes the approximate solution (similar to GMRES) in terms of a Krylov space basis from an upper triangular linear system for the coordinates, and the one where the approximate solutions are updated with a...

A Simpler and Faster Version of Two-Dimensional Gel Electrophoresis Using Vertical, Mini SDS-PAGE Apparatus

We have modified one of the most useful methods of protein separation; namely, two dimensional gel electrophoresis (2-DE). This modified version of 2-DE is not only simpler and easier but also faster than all the currently available methods. In this method, isoelectric focusing is carried out in the first dimension using a vertical sodium dodecyl sulfate polyacrylamide gel electrop...

A Parallel Gmres Version for General Sparse Matrices

This paper describes the implementation of a parallel variant of GMRES on Paragon. This variant builds an orthonormal Krylov basis in two steps: it first computes a Newton basis then orthogonalises it. The first step requires matrix-vector products with a general sparse unsymmetric matrix and the second step is a QR factorisation of a rectangular matrix with few long vectors. The algorithm has ...

Parataxis and Simpler Syntax (re-revised final version w-refs)