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. / Graduation date: 1994
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/35885 |
| Date | 08 June 1993 |
| Creators | Limmer, Douglas J. |
| Contributors | Robson, Robert O. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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