Mathematical Aspects of Scientific Software
The goal is to survey the impact of scientific software on mathematics. Three types of impacts are identified and several topics from each are discussed in some depth. First is the impact on the structure of mathematics through its role as the scientific tool for problem solving. Scientific software leads to new assessments of what algorithms are, how well they work, and what a solution really is. Second is the initiation of new mathematical endeavors. Numerical computation is already very widely known, we discuss the important future roles of symbolic and geometric computation. Finally, there are particular mathematical problems that arise from scientific software. Examples discussed include round-off errors and the validation of computations, mapping problems and algorithms into machines, and adaptive methods. There is considerable discussion of the shortcommings of mathematics in providing an adequate model for the scientific analysis of scientific software.
KeywordsAdaptive Algorithm Scientific Software Mapping Problem Computational Structure Machine Structure
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