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 …

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 …

A variety of block Krylov subspace methods have been successfully developed for linear
systems and matrix equations. The application of block Krylov methods to compute matrix …

This article introduces randomized block Gram-Schmidt process (RBGS) for QR
decomposition. RBGS extends the single-vector randomized Gram-Schmidt (RGS) algorithm …

The block version of the classical Gram--Schmidt (\tt BCGS) method is often employed to
efficiently compute orthogonal bases for Krylov subspace methods and eigenvalue solvers …

A number of features of today's high-performance computers make it challenging to exploit
these machines fully for computational science. These include increasing core counts but …

A Journey through the History of Numerical Linear Algebra: Back Matter Page 1 Bibliography
[1] A. Abdelfattah, H. Anzt, A. Bouteiller, A. Danalis, JJ Dongarra, M. Gates, A. Haidar, J. Kurzak …

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 …

We analyze an expansion of the generalized block Krylov subspace framework of [Electron.
Trans. Numer. Anal., 47 (2017), pp. 100--126]. This expansion allows the use of low-rank …

Pipelined Krylov subspace methods (also referred to as communication-hiding methods)
have been proposed in the literature as a scalable alternative to classic Krylov subspace …