A Set of GMRES Routines for Real and Complex Arithmetics

In this report we describe the implementations of the GMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of simplicity, flexibility and efficiency the GMRES solvers have been implemented using the reverse communication mechanism for the matrixvector product, the preconditioning and the dot product computations. For distributed memory computation several orthogonalization procedures have been implemented to reduce the cost of the dot product calculation, that is a well-known bottleneck of efficiency for the Krylov methods. Finally the implemented stopping criterion is based on a normwise backward error. After a short presentation of the GMRES methods and of the solution of the least-squares problems in real and complex arithmetic, we give a detailed description of the user interface.