Research Accomplishments and Objectives

This document presents my research accomplishments and objectives as of Spring 2002. The document references and lists most of my publications, so it also serves as an annotated list of publications. In addition, Section 8 discusses my teaching and describes a textbook that I have written. Most of my recent and current research focuses on discrete and computer-architecture-related issues in numerical linear algebra. Section 1 describes my work on combinatorial preconditioning; Section 2 describes my work on parallel algorithms in numerical linear algebra, and Section 3 describes work on cache-efficient and out-ofcore algorithms. Section 4 describes work on sparse direct linear solvers. I plan to continue this research effort in the future. My work on algorithms in numerical linear algebra is motivated both by a desire to find techniques and solutions that are relevant to computational scientists, and by a desire to understand fundamental issues. Consequently, some of my work is theoretical, some is experimental, and some combines both. Making solutions relevant to computational scientists often requires the implementation of algorithms in the form of robust and easy-to-use algorithmic libraries. I have produced several such codes: I participated in the production of a code for IBM’s Parallel Engineering and Scientific Subroutine Library, and I produced a library of out-of-core dense matrix algorithms called SOLAR, a library of sparse linear solvers called TAUCS, as well as a number of smaller codes. Except for the IBM code, the codes a publicly available. TAUCS, the most recent library, includes combinatorial preconditioners, incomplete-Cholesky preconditioners, a number of high-performance sparse direct solvers, and out-of-core sparse direct solvers. In addition to producing codes that computational scientists can use on their own, I also collaborate directly with computational physicists and chemists. For example, I recently collaborated with a computational chemist on an electronic-structure calculation code that required an out-of-core SVD algorithm. I have also conducted research that is not related to numerical linear algebra. This includes work on parallel algorithms and parallel-programming systems, described in Section 5, work on geometric optimization that Section 6 describes, and work on digital typography that Section 7 describes. My research on digital typography resulted in another widely-used and widely deployed piece of code, one that is installed and used on most Linux desktop systems.