Davenport, J., 2012. Program Verification in the presence of complex numbers, functions with branch cuts etc. In: SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, 2012-09-25 - 2012-09-28.
In considering the reliability of numerical programs, it is normal to \limit our study to the semantics dealing with numerical precision" (Martel, 2005) [Mar05]. On the other hand, there is a great deal of work on the reliability of programs that essentially ignores the numerics. The thesis of this paper is that there is a class of problems that fall between these two, which could be described as \does the low-level arithmetic imple- ment the high-level mathematics". Many of these problems arise because mathematics, particularly the mathematics of the complex numbers, is more dicult than expected: for example the complex function log is not continuous, writing down a program to compute an inverse function is more complicated than just solving an equation, and many algebraic simplication rules are not universally valid. The good news is that these problems are theoretically capable of being solved, and are practically close to being solved, but not yet solved, in several real-world examples. However, there is still a long way to go before implementations match the theoretical possibilities.
|Item Type ||Conference or Workshop Items (Paper)|
|Departments||Faculty of Science > Computer Science|
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