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 …

The half-precision (fp16) floating-point format, defined in the 2008 revision of the IEEE
standard for floating-point arithmetic, and a more recently proposed half-precision format …

The need to sum floating-point numbers is ubiquitous in scientific computing. Standard
recursive summation of n summands, often implemented in a blocked form, has a backward …

With the commercial availability of mixed precision hardware, mixed precision GMRES-
based iterative refinement schemes have emerged as popular approaches for solving …

We identify a class of random, dense, n*n matrices for which LU factorization with any form
of pivoting produces a growth factor typically of size at least n/(4\logn) for large n. The …

Block low-rank (BLR) matrices possess a blockwise low-rank property that can be exploited
to reduce the complexity of numerical linear algebra algorithms. The impact of these low …

Kernel methods are known to be effective to analyse complex objects by implicitly
embedding them into some feature space. The approximate class-specific kernel spectral …

A analytic review of major problems and new mathematical and technological discoveries in
methods for solving SLAEs is given. This stage of mathematical modeling is a bottleneck …

Dictionary learning is an important sparse representation algorithm which has been widely
used in machine learning and artificial intelligence. However, for massive data in the big …

Domain decomposition (DD) methods are widely used as preconditioner techniques. Their
effectiveness relies on the choice of a locally constructed coarse space. Thus far, this …