t PUBUCATiONS fl^ United States Department of Commerce I I^^^V" I ^1 I National Institute of Standards and Tectinology NAT L INST. OF STAND 4 TECH R.I.C. A111D3 733115 NIST Special Publication 730 NBS-INA — The Institute for Numerical Analysis - UCLA 1947-1954 Magnus R, Hestenes and John Todd -QC- 100 .U57 #730 1991 C.2 i I NIST Special Publication 730 NBS-INA — The Institute for Numerical Analysis - UCLA 1947-1954 Magnus R. Hestenes John Todd Department of Mathematics Department of Mathematics University of California California Institute of Technology at Los Angeles Pasadena, CA 91109 Los Angeles, CA 90078 Sponsored in part by: The Mathematical Association of America 1529 Eighteenth Street, N.W. Washington, DC 20036 August 1991 U.S. Department of Commerce Robert A. Mosbacher, Secretary National Institute of Standards and Technology John W. Lyons, Director National Institute of Standards U.S. Government Printing Office For sale by the Superintendent and Technology Washington: 1991 of Documents Special Publication 730 U.S. Government Printing Office Natl. Inst. Stand. Technol. Washington, DC 20402 Spec. Publ. 730 182 pages (Aug. 1991) CODEN: NSPUE2 ABSTRACT This is a history of the Institute for Numerical Analysis (INA) with special emphasis on its research program during the period 1947 to 1956. The Institute for Numerical Analysis was located on the campus of the University of California, Los Angeles. It was a section of the National Applied Mathematics Laboratories, which formed the Applied Mathematics Division of the National Bureau of Standards (now the National Institute of Standards and Technology), under the U.S. Department of Commerce. This history of the program at INA is concerned primarily with the development of mathemat- ics pertinent to solving numerical computations. This development could happen only if some mathematicians were proficient in handling the electronic digital computers. To insure that there would be some, INA was constituted. It was well funded, and could attract first class mathemati- cians to take a year off for research at INA. There they were in the midst of people solving problems of considerable difficulty using the digital computers. They were thus enticed into using them. When this happened, many important developments emerged. This history is centered around these people and asks "Who were there?", "What were their interests?", "What did they do?". Key words: differential equations; digital computers; history; linear programming; matrix; numeri- cal analysis; UCLA iii FOREWORD In the 1930's A. M. Turing conceived the idea of a computer. The electronic technology needed to construct a working model did not then exist. However, during World War II great strides were made in electronic technology. Just after World War II there appeared the ENIAC. It was an electronic computer but not of the Turing type. However, the Tiu"ing computer was obvi- ously just around the comer, and would run rings around the ENIAC. It was anticipated that the Turing computer would give much assistance in various mathematical studies. This could happen only if some mathematicians were proficient in handling the Turing com- puter. To assure that there would be some, the Institute for Numerical Analysis (INA) was consti- tuted. It was well funded, and could attract first class mathematicians to take a year off for research at INA. There they were in the midst of people solving problems of considerable difficialty by the use of the Turing computers. They were enticed into learning to use them. When this happened, many important developments emerged, as recounted in the history that follows. Summer 1985 J. Baridey Rosser Professor Emeritus Center for Mathematical Sciences University of Wisconsin, Madison V ( I PREFACE Over 30 years have passed since the events described in this History took place. We have recounted them to the best of our recollection and apologize for our sins of omission and commis- sion. We have given references to our sources and the material which we have used will be de- posited in appropriate places. The Quarterly Progress Reports and internal memoranda of the Institute for Numerical Analysis (INA) were particularly useful. Attention is invited to the Proceed- ings of the 1987 Princeton Conference [131] in which the articles by G. B. Dantzig and ourselves are particularly relevant. Our point of view is probably biased towards the West and may not represent the official Washington attitude. Further, in part because the original sponsor of the writing is the Mathemati- cal Association of America, we have stressed the research and educational aspects of the program, rather than the machine development and computational service aspects, although they had imdeni- able importance. Finally, our selection of topics for more detailed discussion is undoubtedly differ- ent from that of others who might have undertaken this work— differential equations, Monte Carlo, combinatorics, number theory could well have been emphasized more. We are grateful to many of our former colleagues who shared their reminiscences with us, and we are grateful for the opportunity to communicate to a wider public some account of what was an exciting time for both of us. The machine development aspect of INA has been well documented. A short history of this development is reproduced in Appendix C. This history was written by H. D. Huskey, who was responsible for the building of the SWAC, the National Bureau of Standards Western Automatic Computer. There is, however, no adequate documentation of the research aspect of INA. Accord- ingly, we give here a history of the program at INA concerned primarily with the development of mathematics pertinent to solving problems involving numerical computations. We include abbrevi- ated remarks about other aspects of the program at INA. Our story is centered around people. We ask "Who were there?", "What were their interests?", "What did they do?". We give only selected answers to the questions with the hope that they are sufficient to give a bird's-eye view of the program at INA. In a sense the researchers at INA pioneered in modern numerical analysis. "Graduates" of INA are scattered all over the United States and elsewhere. They have done much to promote the development of numerical mathematics pertinent for use of computing machines for scientific and educational purposes. We wish to single out for special mention three persons who played a dominant role in the formation and maintenance of INA. They are E. U. Condon, John H. Curtiss, and Mina Rees. Condon was the Director of the National Bureau of Standards (NBS) and was an enthusiastic supporter of the project. He gave the "go ahead" for Curtiss to set up INA as part of the Applied Mathematics Program of the NBS. Curtiss was the guiding force of the INA project and was instrimiental in interesting prominent mathematicians to participate in the program. Mina Rees was the Head of the Mathematics Branch of the Office of Naval Research (ONR). She was one of a group which saw need for the development of "machine" mathematics and encouraged Curtiss to proceed with his program. She was instrumental in arranging substantial financial support by ONR for the INA project. In fact, ONR funded the major portion of the mathematical research program of INA. The machine development program was largely supported by the Air Force. Contributions to this program were also made by the Army. These governmental agencies played an important role in the formation of INA. There are several mathematicians to whom we are especially grateful for their help in the preparation of this volume. First, Olga Taussky-Todd, who was one of the original crew in 1947-48 and was a consultant to the NBS Applied Mathematics Division (AMD) from 1949 to 1957. Her vii wide knowledge of mathematics and mathematicians played an important part in the development of NBS-INA, as will become apparent in our history. In addition, her outstanding memory and her collection of INA photographs have been invaluable during the preparation of this history. We are also indebted to Marion I. Walter, who was at INA in 1952-53 for her extensive collection of INA photographs. We also acknowledge the permissions to reproduce published photographs which have been given by various organizations and individuals. We appreciate comments on drafts of our manuscripts by E. W. Cannon, C. R. De Prima, and J. H. Wilkinson. Finally we appreciate greatly the work of Churchill Eisenhart and Joan Rosenblatt who care- fully read our manuscript and tried to make m historians of science and of Shirley Bremer who collated and checked all the changes and corrections and acted as our representative with the NBS production staff who, imder the direction of Don Baker, Rebecca Pardee, and Ernestine Gladden, did a splendid job. M. R. Hestenes John Todd UCLA Caltech Los Angeles, CA 90024 Pasadena, CA 91125 viii CONTENTS Page FOREWORD iu PREFACE V CHAPTER I The Beginnings 1 The War Years - 1939-1945 2 The Post-War Years 3 CHAPTER II The Period Summer 1947 through Summer 1948 7 CHAPTER III The Period Fall 1948 through Spring 1949 11 CHAPTER IV The Period Summer 1949 through Summer 1950 17 CHAPTER V The Period Fall 1950 through Spring 1951 23 CHAPTER VI The Period Summer 1951 through Spring 1952 27 CHAPTER VII The Period Summer 1952 through Spring 1953 33 CHAPTER VIII The Period Summer 1953 through Spring 1954 39 CHAPTER IX Some Typical Projects 45 Hilbert Matrices and Related Topics 45 Gerschgorin Theorems and Related Results 47 Solutions of Systems of Linear Equations 48 REFERENCES 67 PHOTOGRAPHS AND CARTOONS 73 APPENDIX A. John Hamilton Curtiss 1909-77 A-1 APPENDIX B. Two Papers by John H. Curtiss B-1 APPENDIX C. TheSWAC C-1 APPENDIX D.