I. Norman Katz
Professor
Norman
Katz received his bachelor’s and master’s degrees in
mathematics in 1952 and 1954 from Yeshiva University in New York
City. He received his doctorate in mathematics in 1959 from the
Massachusetts Institute of Technology.
From 1959 to 1967, he was at the AVCO Research and Advanced Development in Wilmington, Massachusetts, first as a Senior Scientist; then as a Section Chief; and finally as manager of the mathematics department. He studied numerical solutions of engineering problems, particularly ordinary and differential equations, on high speed computers.
In 1967, he joined Washington University as an associate professor in the Department of Applied Mathematics and Computer Science. In 1974, he joined the Department of Systems Science and Mathematics and was promoted to professor. In 1991, he become chair of the department. He also served as a consultant at McDonnell Aircraft Company from 1980 to 1990.
Numerical analysis and computational mathematics have become increasingly active and important disciplines pervading science, engineering, and mathematics. Norman Katz’s research interests are in the numerical solution of ordinary and partial differential equations, reliable algorithms, parallel computation and finite element analysis. For more than 20 years, he has helped develop the p-version of the finite element method. This version is now widely accepted as a reliable computational tool in the finite element analysis of elastic structures, heat transfer, and related fields, and is implemented in many commercial computer codes.
Current research in this area focuses on multi-p methods; these are promising new iterative methods for solving the large systems of linear equations that arise in the p-version, particularly for problems in three dimensions. He also studies the effective implementation of our algorithm on parallel processors.
He and his students have formulated new algorithms guaranteed to be reliable, for solving certain nonlinear equations. Study is continuing to expand the range of applicability of our approach.
Recently, he has begun to develop algorithms for numerically solving the Hamilton-Jacobi-Bellman equations, which arise in the control of nonlinear dynamic systems. The solution to these equations, which may have special features including cusp-like behavior, provide optimal control laws for many important engineering problems.
Professional Activities
-Member of American Mathematical Society (AMS)
-Society of Industrial and Applied Mathematics (SIAM)
-Mathematical Association of America
-Institute for Operations Research and Management Science (INFORMS)
-Reviewer and Associate Editor for various professional journals
-Lecturer for the Visiting Mathematics
Lecturer Program (Sponsored by the Missouri Section of the Mathematical Association of America)
Awards and Honors
-Washington University Founders Day Award (1984)
-Burlington Northern Foundation Faculty Achievement Award (1991)
Selected Publications