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 …

In recent years, a new kind of accelerated hardware has gained popularity in the artificial
intelligence (AI) community which enables extremely high-performance tensor contractions …

One can simulate low-precision floating-point arithmetic via software by executing each
arithmetic operation in hardware and then rounding the result to the desired number of …

We consider the computation of the Euclidean (or L2) norm of an n-dimensional vector in
floating-point arithmetic. We review the classical solutions used to avoid spurious overflow …

Randomized projection methods have been shown to be very efficient at computing low-
rank approximations (LRA) of large matrices. In this work, we investigate the design and …

Many special hardware units, such as Matrix Core and Tensor Core, have recently been
designed and applied in various scientific computing scenarios. These units support tensor …

Density matrix perturbation theory based on recursive Fermi-operator expansions provides a
computationally efficient framework for time-independent response calculations in quantum …

In this paper we develop the first fine-grained rounding error analysis of finite element (FE)
cell kernels and assembly. The theory includes mixed-precision implementations and …

The explosive demand for artificial intelligence (AI) workloads has led to a significant
increase in silicon area dedicated to lower-precision computations on recent high …

In the literature on algorithms for computing multi-term addition in floating-point arithmetic it
is often shown that a hardware unit that has single normalization and rounding improves …