Computation of the Latent Roots of a Hessenberg Matrix by Bairstow's Method

published the two groups in English Electric can go ahead with their respective translators, each with its separate field of application. Somebody mentioned recursive procedures, and people playing with them. Most published examples show you how to do this—for instance, the famous factorial example— and it would be difficult to think of a less efficient procedure for factorial than this. However, if you have a procedure, written by somebody else, which uses, say, an integration routine, it would be possible to use this procedure, even within the integration routine, without having to delve into the procedure. That is the real benefit of recursive procedures. Mr. F. S. Ellis (Elliott Brothers): Dr. Dijkstra has quoted certain ratios in connection with ALGOL programs and handwritten programs. Can he give the corresponding ratios in time involved in writing the handwritten programs and the ALGOL programs? Mr. Glennie quoted a figure of 3 to 1 in cost, but what about time? Do you more than make up for the difference in cost by the saving in time? Dr. Dijkstra: The corresponding ratios in writing time might be 100 or 1,000. It goes up on an exponential scale in practice. That is why so few comparisons with run-time systems are available. Mr. Glennie: The difficulty of answering questions as to the effect of ALGOL and FORTRAN on programming times is that there is no such thing as a standardized programmer. But I would say that you might expect to get a gain of 2 or 3 to 1 with FORTRAN with the average programmer, assuming the problems were defined. The Chairman: I am sorry to have to draw this discussion to a close, but we have to meet again at 2 o'clock. I know that you would wish me to add your thanks to mine, to our four speakers. We are indebted to Dr. Dijkstra, Mr. Hoare, Mr. Duncan and Mr. Glennie for making this morning's session a great success. Thank you very much. (The conference adjourned.)