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 …

Since the end of the 19th century, radioelectronic devices (REDs) have actively penetrated
into all modern community spheres. Achievements in the fields of radio engineering and …

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 …

Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …

Abstract A High Performance Computing alternative to traditional Krylov subspace methods,
pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared …

In this paper, we present a comprehensive framework for studying Krylov subspace methods
used to solve the linear system A x= f. These methods aim to achieve convergence within a …

Communication, ie, moving data between levels of a memory hierarchy or between
processors over a network, is much more expensive (in time or energy) than arithmetic …

Krylov subspace methods are among the most efficient solvers for large scale linear algebra
problems. Nevertheless, classic Krylov subspace algorithms do not scale well on massively …

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 …

This article derives trade-offs between three basic costs of a parallel algorithm:
synchronization, data movement, and computational cost. These trade-offs are lower bounds …