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Part I Case for Support Computing with arbitrary precision curves

By Dr. Michal Konečn´y

Abstract

Previous research track record and plans for the future The proposer has a long-standing interest in the theory and applications of computing with arbitrary precision (AP), which began with his PhD training (1996–2000) at the University of Birmingham under the supervision of Prof. Jung. PhD thesis. The thesis (Konečn´y 2000) built on the work of Wiedmer, Weihrauch, Edalat, Ko and others on representing real numbers as infinite streams of digits in an arbitrary precision computation. The thesis addressed, in this context, one of the first fundamental questions in computational complexity theory: Which real-number functions can be computed to an arbitrary precision without an ever growing need for more memory? This question was answered for many different ways of representing the real numbers as infinite streams of symbols and for all reasonably well-behaved functions (in some precise sense). This result is also described and proved in two journal articles (Konečn´y 2004, Konečn´y 2002), each for different types of real-number representations. The thesis extends the articles in terms of the scope of representations and also generalises the theorem in another direction. It covers not only functions but also one-to-many mappings. Such mappings arise naturally from the fact that each real number can be represented in many ways: for different representations of the same arguments different, but all correct results may be computed. More importantly, some frequently occurring practical problems, such as finding a zero of a polynomial, cannot be computed as a function but rather as a one-tomany mapping. Work in Edinburgh. More recently, the proposer worked as a research fellow for the EPSRC funded project “Typ

Year: 2004
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