In this survey paper, we compare native double precision solvers with emulated-and mixed-
precision solvers of linear systems of equations as they typically arise in finite element …

The efficient utilization of mixed-precision numerical linear algebra algorithms can offer
attractive acceleration to scientific computing applications. Especially with the hardware …

Randomized numerical linear algebra-RandNLA, for short-concerns the use of
randomization as a resource to develop improved algorithms for large-scale linear algebra …

Work on this book started more than 15 years ago, when I began a revision of a textbook
from 1974 on numerical methods. That book devoted only about 90 pages to matrix …

As the standard method for solving systems of linear equations, Gaussian elimination (GE) is
one of the most important and ubiquitous numerical algorithms. However, its successful use …

On modern architectures, the performance of 32-bit operations is often at least twice as fast
as the performance of 64-bit operations. By using a combination of 32-bit and 64-bit floating …

Iterative refinement is a long-standing technique for improving the accuracy of a computed
solution to a nonsingular linear system Ax=b obtained via LU factorization. It makes use of …

What if things had a voice? What if we could talk directly to things instead of using a
mediating voice interface such as an Alexa or a Google Assistant? In this paper, we share …

Recent versions of microprocessors exhibit performance characteristics for 32 bit floating
point arithmetic (single precision) that is substantially higher than 64 bit floating point …

Managing error has become an increasingly central and contested arena within data
science work. While recent scholarship in artificial intelligence and machine learning has …