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Symbolic Computation

Eleven of my papers are primarily concerned with symbolic computation: two are `purely' symbolic, four apply symbolics to numerics or vice-versa, and five are applications of symbolic computation to real problems (low Reynolds number flow or heat transfer---I count the flow-induced vibration papers separately). Just by number of papers per area, then, symbolic computation is my primary area (especially when you consider that most of my other papers use symbolic computation, often in nontrivial ways).

The most important symbolic paper I have written (if I have to make a choice) is ``The Singular Value Decomposition for Polynomial Systems'', written with Patrizia Gianni, Barry Trager, and Stephen Watt, while I was at IBM T. J. Watson. This paper applies ideas from numerical analysis, namely backward error and the SVD, to problems in symbolic computation, and details linear algebraic methods for solving polynomial problems. This paper has received a lot of interest (I was invited to Amsterdam, to Spain, and to New York on the strength of it) and is on a currently `hot' topic, with applications to Computer-Aided Design among other things.

I am now also moving in to the idea of using computer algebra to create special-purpose numerical methods, and with Jacek Rokicki have developed a program to generate finite-difference formulas, which has allowed us to create new and extremely efficient methods for some problems. This research has not yet `taken off', but I think it will.

Rob Corless
Sun Dec 3 19:24:27 PST 1995