Conjugacy and gradients in variational theory and analysis
Magnus Rudolph Hestenes · 1987
I have been invited to describe my experiences in the field of numerical analysis and to describe how these experiences influenced me in my studies of mathematics.In particular, I was invited to tell the story of the development of the conjugate gradient method for solving linear systems.I was one of the originators of this method.At the invitation of the Mathematical Association of America, John Todd and I have written a short history of the Institute for Numerical Analysis, 1947-1954, located on the campus of UCLA.This Institute, called INA, was a Section of the National Applied Mathematical Laboratories, which formed the Applied Mathematics Division of the National Bureau of Standards, a part of the Department of Commerce.In this brief history we were concerned mainly with the mathematical aspects of this program.In particular, we were concerned about who participated in the project, what did they do, and what was their University affiliation.It is not my intention to repeat the material presented in this history except perhaps for some special items of interest.As many of you know my specialty in mathematics is Variational Theory and Optimal Control Theory.My experiences in these fields have greatly influenced my approach to problems in numerical analysis.I shall describe certain aspects of Variational Theory, which are not only of interest in themselves but which led to a method of attack of certain computational problems.