Chapter 19 Excerpted from the 1994 Research Summary
(Copyright 1994, UC Regents)

Contact person: Carol Block, ILP Coordinator
(ilp@hera.eecs.berkeley.edu)
510.643-6691, 643-6694 fax


In the Computer Sciences Division of EECS, Professors Demmel, Fateman,
Kahan, and Parlett work on the infrastructure that supports computer
users and their scientific applications. Their work in this department
complements the strengths of other departments, like Mathematics, in
which Professors Demmel, Kahan, and Parlett are jointly appointed in
numerical analysis and its applications.

Professor Kahan won the 1989 A.M. Turing Award of the ACM for, among
other things, his role in the design of the ANSI/IEEE standard 754-1985
for floating-point arithmetic in computers. Before 1980, when the IEEE
Floating Point Arithmetic standard began to influence arithmetic
design,  every computer manufacturer supplied his own mathematical
library of elementary functions like EXP and COS. These libraries
varied widely in quality, but tended on average to be superior in speed
and/or accuracy to the rather poor "portable" libraries that came
with C and UNIX. After 1985, when Prof. Kahan's students produced most
of a portable mathematical library for 4.3 BSD UNIX running on machines
that conform to IEEE 754, the situation changed. That library was
distributed and copied very widely (for instance, by IBM on its first
RISC-based products) because of its high quality. Subsequent
improvements, some published and others immenently to be published,
have pushed both speed and accuracy beyond the best available on a few
computers before 1980, but now available to practically everybody.
Currently, work on a few non-elementary functions like GAMMA and ERF
continue to be pursued by Prof. Kahan's students and ex-students.

Prof. Kahan also collaborates on numerical libraries like LAPACK with
his colleagues, Profs. Demmel and Parlett, and their students. He has
turned his attention especially to the handling of exceptions like
division-by-zero, over/underflow and sqrt(negative). These exceptions
cannot be dismissed cavalierly as programming errors without
jeopardizing our ability to manage concurrent (parallel) computation
efficiently. Prof. Kahan also shares with Prof. Fateman an intense
interest in computerized symbolic algebra and analysis. Professor Kahan
is also currently working on unconventional numerical ODE algorithms
that are efficient for problems arising in chemical kinetics and
celestial mechanics.

Professor Fateman heads a project to improve algebraic computation
capabilities on interactive scientific workstations. This work includes
the development of algorithms that can exploit parallelism in
time-consuming symbolic computations. Other activities include the
development of techniques for improved environments for combined
symbolic and numerical techniques for problem-solving, and of
interactive proofs of the correctness of manipulations.

Another project explores the use of large memory systems in the
generation, storage, and retrieval of tables of integrals and similar
formulas.

Professor Parlett and his students are concentrating on solving large
systems of equations (over 1000 degrees of freedom), large 
generalized eigenvalue problems, and the computation of the
exponential of small matrices (n <= 50). Problems like these arise in
the static and dynamic analysis of plastic structures, electric
circuits, models of a country's economy, and certain chemical plants.
The project on computing the matrix exponential is complete, except
for testing and documentation. Reliable and black-box implementations
of the Lanczos algorithm are also in the testing stage. This code
solves the general linear eigenvalue problem and allows the mass
matrix to be singular, that is, infinite eigenvalues do not hinder
the calculation of the finite ones.

Professor Demmel, appointed to EECS and Mathematics in spring 1990,
participates in a variety of programs, some carried over from his
previous work at New York University's Courant Institute.  His current
research focuses on the LAPACK project, which is producing linear
algebra software for high performance computers. The first LAPACK
release in February 1992 was for vector machines, shared memory
parallel computers, and high performance workstations. The second
release will address the harder problem of distributed memory machines
like the Thinking Machines CM-5 and Intel Paragon. It will have
software for sparse matrices as well as dense matrices. This is joint
work with Profs. Kahan and Parlett, Prof. Jack Dongarra and Dr. David
Walker at the University of Tennessee, Prof. Dan Sorensen at Rice
University, and Prof. Michael Heath at the University of Illinois. In
addition, he is parallelizing a global atmospheric chemistry model, as
part of a NASA/HPCC-funded effort to model the earth's climate.