Algorithmic bombardment for the iterative solution of linear systems: a poly-iterative approach

TL;DR: The context, design, and recent development of the LAPACK for clusters (LFC) project is described, developed in the framework of Self-Adapting Numerical Software (SANS), which believes such an approach can deliver the convenience and ease of use of existing sequential environments bundled with the power and versatility of highly tuned parallel codes that execute on clusters.

TL;DR: Here three algorithms simultaneously are applied simultaneously to the system, in the hope that at least one will converge to the solution, and the cost of three methods can be reduced to that of a single method.

TL;DR: Petascale computing is capable of driving the next decade of research in high-performance computing and communications and will require advances across all aspects of it.

TL;DR: In this paper, a recursive method for the LU factorization of sparse matrices is described, and performance results show that the recursive approach may perform comparable to leading software packages for sparse matrix factorization in terms of execution time, memory usage and error estimates of the solution.

TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.

TL;DR: Numerical experiments indicate that the new variant of Bi-CG, named Bi- CGSTAB, is often much more efficient than CG-S, so that in some cases rounding errors can even result in severe cancellation effects in the solution.

TL;DR: In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist.

TL;DR: The PVM system, a heterogeneous network computing trends in distributed computing PVM overview other packages, and troubleshooting: geting PVM installed getting PVM running compiling applications running applications debugging and tracing debugging the system.