When simulating a mechanism from science or engineering, or an industrial process, one is
frequently required to construct a mathematical model, and then resolve this model …

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 …

The mathematical theory of Krylov subspace methods with a focus on solving systems of
linear algebraic equations is given a detailed treatment in this principles-based book …

We present parallel and sequential dense QR factorization algorithms that are both optimal
(up to polylogarithmic factors) in the amount of communication they perform and just as …

The performance of CPU-based and GPU-based systems is often low for PDE codes, where
large, sparse, and often structured systems of linear equations must be solved. Iterative …

Aiming at the current problems that most physical hosts in the cloud data center are so
overloaded that it makes the whole cloud data center'load imbalanced and that existing load …

The solution of large sparse linear systems arises in many applications, such as
computational fluid dynamics and oil reservoir simulation. In realistic cases the matrices are …

Scalability of Krylov subspace methods suffers from costly global synchronization steps that
arise in dot-products and norm calculations on parallel machines. In this work, a modified …

Unlike traditional dark silicon works that attack the computing logic, this article puts a focus
on the memory part, which dissipates most of the energy for memory-bound CPU …

Abstract Block Gram-Schmidt algorithms serve as essential kernels in many scientific
computing applications, but for many commonly used variants, a rigorous treatment of their …