Designing algorithms in linear algebra for different computer architectures

Architectures of future machines promise to offer a profusion of computing environments. The existing forerunners have already given many software developers cause to reexamine the underlying algorithms for efficiency sake. However, it seems to be an unnecessary waste of effort to recast algorithms with only one computer in mind, regardless of how fast that one may be. With such a wide variety of computer systems and architectures in use or proposed, the challenge for people designing algorithms is to develop algorithms and ultimately software that are both efficient and portable. In this talk we will discuss implementations and performance of a few standard algorithms from linear algebra on high performance computers, such as the CRAY 1, CRAY X-MP, Fujitsu VP-200, Hitachi S-810/20 and Denelcor HEP based on the use of high-level modules. High-level modularity facilitates portability and aids in attaining performance efficiency on a wide variety of environments spanning scalar, vector, and certain parallel computers.