High-Performance Algorithms for Numerical Linear Algebra

Abstract

Matrix computations lie at the heart of many scientific computations. While sophisticated algorithms have been established for various numerical linear algebra problems such as the solution of linear simultaneous equations and eigenvalue problems, they require considerable modification with the advent of exaFLOPS- scale supercomputers, which are expected to have a huge number of computing cores, deep memory hierarchy, and increased probability of hardware errors. In this chapter, we discuss projected hardware characteristics of exaFLOPS machines and summarize the challenges to be faced by numerical linear algebra algorithms in the near future. Based on these preparations, we present a brief survey of recent research efforts in the field of numerical linear algebra targeted at meeting these challenges.