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

Today's floating-point arithmetic landscape is broader than ever. While scientific computing
has traditionally used single precision and double precision floating-point arithmetics, half …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

Double-precision floating-point arithmetic (FP64) has been the de facto standard for
engineering and scientific simulations for several decades. Problem complexity and the …

Computing units that carry out a fused multiply-add (FMA) operation with matrix arguments,
referred to as tensor units by some vendors, have great potential for use in scientific …

Integrating renewable resources within the transmission grid at a wide scale poses
significant challenges for economic dispatch as it requires analysis with more optimization …

Large sparse linear systems of equations are ubiquitous in science, engineering and
beyond. This open access monograph focuses on factorization algorithms for solving such …

We introduce a novel approach to exploit mixed precision arithmetic for low-rank
approximations. Our approach is based on the observation that singular vectors associated …

GMRES-based iterative refinement in three precisions (GMRES-IR3), proposed by Carson
and Higham in 2018, uses a low precision LU factorization to accelerate the solution of a …

What is the fastest way to solve a linear system Ax=b in arithmetic of a given precision when
A is symmetric positive definite and otherwise unstructured? The usual answer is by …