Recent Developments in Dense Numerical Linear Algebra
Nicholas John Higham · 1997
Abstract Numerical linear algebra with dense matrices is still today, as it was at the time of the first IMA meeting on the State of the Art in Numerical Analysis in 1965, an extremely active area of research. There are several reasons. First, we still do not fully understand some of the classical algorithms. For example, the behaviour of the growth factors for Gaussian elimination and its variants with partial and complete pivoting is not yet completely understood. Second, novel computer architectures force us to design new algorithms, modify old ones, and reassess algorithms that were once discarded. In particular, parallel computers have made the flop counts traditionally used to measure the cost of an algorithm of dubious relevance, so that some algorithms hitherto considered inefficient are now of interest again. Third, applications stimulate the development of new theory and techniques. For example, real-time signal processing applications have stimulated much work on rank-revealing factorizations and the updating of factorizations after low rank changes.