The traditional metric for the efficiency of a numerical algorithm has been the number of
arithmetic operations it performs. Technological trends have long been reducing the time to …

This paper is about GMRES algorithms for the solution of nonsingular linear systems. We
first consider basic algorithms and study their convergence. We then focus on acceleration …

Krylov subspace methods (KSMs) are iterative algorithms for solving large, sparse linear
systems and eigenvalue problems. Current KSMs rely on sparse matrix-vector multiply …

Data communication within the memory system of a single processor node and between
multiple nodes in a system is the bottleneck in many iterative sparse matrix solvers like CG …

The performance of sparse iterative solvers is typically limited by sparse matrix-vector
multiplication, which is itself limited by memory system and network performance. As the gap …

Advancements in the field of high-performance scientific computing are necessary to
address the most important challenges we face in the 21st century. From physical modeling …

For the last decade, the exponential potential of Moore's Law has been squandered in the
effort to increase single thread performance, which is now limited by the memory, instruction …

Krylov subspace methods are iterative methods for solving large, sparse linear systems and
eigenvalue problems in a variety of scientific domains. On modern computer architectures …

Krylov subspace projection methods are widely used iterative methods for solving large-
scale linear systems of equations. Researchers have demonstrated that communication …

Krylov subspace methods are a popular class of iterative methods for solving linear systems
with large, sparse matrices. On modern computer architectures, both sequential and parallel …