Nick Higham 
An eigenvalue of a square matrix is a scalar such that for some nonzero vector . The vector is an eigenvector of and it has the distinction of being a direction that is not changed on multiplication by . An … Read more
In numerical linear algebra we are concerned with solving linear algebra problems accurately and efficiently and understanding the sensitivity of the problems to perturbations. We describe seven sins, whereby accuracy or efficiency is lost or misleading information about sensitivity is … Read more
Six matrix factorizations dominate in numerical linear algebra and matrix analysis: for most purposes one of them is sufficient for the task at hand. We summarize them here. For each factorization we give the cost in flops for the standard … Read more
The Fugaku supercomputer that tops the HPL-AI mixed-precision benchmark in the June 2021 TOP500 list. It solved a linear system of order 10^7 using IEEE half precision arithmetic for most of the computations. The largest dense linear systems being solved … Read more