Efficient Gram-Schmidt orthonormalisation on parallel computers

This paper compares the parallel efficiency of three Gram-Schmidt orthonorm alization algorithms: modified Gram-Schmidt, classical Gram-Schmidt, and it erated classical Gram-Schmidt. The paper shows how these algorithms can be implemented on a parallel computer, and how their communication overhead ca n be minimized. In addition, it briefly examines the numerical properties o f these algorithms. Finally, it provides some guidelines for selecting the most appropriate algorithm. Copyright (C) 2000 John Wiley & Sons, Ltd.