Using p-adic valuations to decrease computational error Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/v692t984h

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  • The standard way of representing numbers on computers gives rise to errors which increase as computations progress. Using p-adic valuations can reduce error accumulation. Valuation theory tells us that p-adic and standard valuations cannot be directly compared. The p-adic valuation can, however, be used in an indirect way. This gives a method of doing arithmetic on a subset of the rational numbers without any error. This exactness is highly desirable, and can be used to solve certain kinds of problems which the standard valuation cannot conveniently handle. Programming a computer to use these p-adic numbers is not difficult, and in fact uses computer resources similar to the standard floating-point representation for real numbers. This thesis develops the theory of p-adic valuations, discusses their implementation, and gives some examples where p-adic numbers achieve better results than normal computer computation.
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