Sparse solvers provide essential functionality for a wide variety of scientific applications.
Highly parallel sparse solvers are essential for continuing advances in high-fidelity, multi …

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 …

We investigate two single-reduce orthogonalization schemes for both s-step and pipelined
GMRES. The first is based on classical Gram Schmidt with reorthogonalization (CGS2), and …

We compare the performance of pipelined and s-step GMRES, respectively referred to as l-
GMRES and s-GMRES, on distributed multicore CPUs. Compared to standard GMRES, s …

Parallel implementations of linear iterative solvers generally alternate between phases of
data exchange and phases of local computation. Increasingly large problem sizes and more …

The multiplication of a sparse matrix with a dense vector (SpMV) is a key component in
many numerical schemes and its performance is known to be severely limited by main …

We consider Anderson extrapolation to accelerate the (stationary) Richardson iterative
method for sparse linear systems. Using an Anderson mixing at periodic intervals, we …

The performance of Krylov subspace methods on large-scale parallel computers is often
limited by communication, or movement of data. This has inspired the development of s-step …

Sparse linear iterative solvers are essential for many large-scale simulations. Much of the
runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a …

The s-step Conjugate Gradient (CG) algorithm has the potential to reduce the
communication cost of standard CG by a factor of s. However, though mathematically …