An Experimental Algorithm for N-Dimensional Adaptive Quadrature
ACM Transactions on Mathematical Software (TOMS)
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Although I have been involved in the development of programs for numerical evaluation of integrals for a number of years, it was only recently that I became aware of the importance of providing such tools in BASIC. I admit to having had a built-in predjudice against people using BASIC. To me it seemed that these people were either solving trivial problems, or were too lazy to learn FORTRAN. But in the last year or so, I have been made aware that BASIC is very much an alive language with sophisticated scientific users. The growth in popularity of the microcomputer is partly responsible for this. At NBS I also see many more scientists who are not as computer oriented as those I met at Los Alamos and this has some effect too. In this talk I would like to describe a few important quadrature techniques that are essential to have and how they can be best implemented in BASIC. This seems to me a rather neglected area. There may be a few odd bits of software around in BASIC, but most are not what I would call state-of-the-art. If I am wrong about this I would be happy to be corrected. We could publish a bibliography of such programs here in the SIGNUM Newsletter. In the first section, as a convenience to those of us who are not very familiar with the language, I outline several of the differences with FORTRAN.