Sunday, Full Day
Title: High-Performance Numerical Linear Algebra: Fast and Robust Kernels for Scientific Computing
Presenters: Jack Dongarra, University of Tennessee; Iain Duff, Rutherford Appleton Laboratory; Danny Sorensen, Rice University; Henk van der Vorst, Utrecht Rutherford Appleton Laboratory University
Level: 20% Introductory | 50% Intermediate | 30% Advanced
Present computers, even workstations and personal computers, allow the solution of very large-scale problems in science and engineering. A major part of the computational effort goes in solving linear algebra subproblems. We will discuss a variety of algorithms for these problems indicating where each is appropriate and emphasizing their efficient implementation. Many of the sequential algorithms used satisfactorily on traditional machines fail to exploit the architecture of modern computers. We will consider techniques devised to utilize modern architectures more fully, especially the design of the Level 1, 2, 3 BLAS, LAPACK and ScaLAPACK.
For large sparse linear systems we will give an introduction to this field and guidelines on the selection of appropriate software. We will consider both direct methods and iterative methods of solution. In the case of direct methods, we will emphasize frontal and multifrontal methods including variants performing well on parallel machines. For iterative methods, our discussion will include CG, MINRES, SYMMLQ, BiCG, QMR, CGS, BiCGSTAB, GMRES, and LSQR. For large-sparse eigenproblems we will discuss some of the most widely used methods such as Lanczos, Arnoldi, and Jacobi-Davidson. The Implicitly Restarted Arnoldi Method will be introduced along with the software ARPACK that is based upon that method.