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From 1959 to 1967, Professor Katz 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, Professor Katz joined Washington University in St. Louis as an associate professor in the Department of Applied Mathematics and Computer Science. In 1991, he became 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. Professor Katz's primary 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. Other research interests include formulation and solution of location - equilibrium problems widely used in optimal facility location.