Pacheco ABSTRACT: NSF/CBMS Regional Conference #9414856 "Numerical Linear Algebra on Parallel Processors" In most branches of science and engineering, numerical linear algebra plays a central role in the solution of problems by computer. The reason for this is that scientists and engineers usually solve nonlinear problems by reducing them to a sequence of linear problems. Thus considerable attention has been devoted to the development of efficient methods for solving problems in linear algebra on computers. Within the last ten years, the advent of parallel processing has resulted in enormous additional growth in research into numerical linear algebra, since many of the methods used on conventional computers are inefficient when used on parallel machines. As a consequence of this growth in research, it is extremely difficult for researchers and students to keep abreast of the state of the art. Thus there is a great need for someone to provide a comprehensive view of the current state of the art and anticipated future developments. This comprehensive view is especially important now because there is a fairly clear consensus about architectures for parallel machines and an emerging consensus about many issues related to software. In order to provide such a comprehensive view of parallel numerical linear algebra and to stimulate further research into the field, an NSF/CBMS Regional Conference will be held at the University of San Francisco during the week of June 12, 1995, with Professor James W. Demmel as the principal lecturer. Professor Demmel will begin by discussing parallel architectures and parallel software. He will continue with a discussion of parallel algorithms for dense matrices. This will include a discussion of parallel algorithms for matrix multiplication, Gaussian elimination, the solution of least squares problems and the calculation of eigenvalues and eigenvectors. He will also lecture on parallel algorithms for sparse ma trices. These lectures will cover direct and iterative methods; they will discuss algorithms for partitioning sparse matrices, Cholesky factorization, GMRES, QMR, and the Lanczos and Arnoldi methods. Professor Demmel's lectures will be supplemented by lectures by several other specialists in the field. These supplementary lectures will cover multifrontal methods for matrix factorization, domain decomposition methods, parallel finite elements, graph partitioning, and applications.
