On the Foundations of Computational Mathematics

Publisher Summary This chapter discusses the interaction of computational numerical with pure mathematics.. As far as computer scientists are concerned, their genuine “interface of interaction” with numerical thinking is in two distinct areas: complexity theory and high-performance computing. While complexity theory has always been a glamourous activity in theoretical computer science, it has only recently emerged as a focus of concerted activity in numerical circles, occasionally leading to a measure of acrimony. It is to be hoped that, eventually, computer scientists will find complexity issues involving real-number computations to be challenging, worthwhile, and central to the understanding of theoretical computation. Likewise, the ongoing development of parallel computer architectures and the computational grid is likely to lead to considerably better numerical/computational interaction at the more practical, engineering-oriented end.

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