Computations with Eeective Real Numbers
نویسنده
چکیده
A real number x is said to be eeective if there exists an algorithm which, given a required tolerance " 2 Z 2 Z , returns a binary approximation x ~ 2 Z 2 Z for x with jx ~ ? xj < ". In this paper, we review several techniques for computations with such numbers, and we will present some new ones.
منابع مشابه
Computable Real Functions : Type 1
Based on the Turing machine model there are essentially two diierent notions of computable functions over the real numbers. The eeective functions are deened only on computable real numbers and are Type 1 computable with respect to a numbering of the computable real numbers. The eeectively continuous functions may be deened on arbitrary real nunbers. They are exactly those functions which are T...
متن کاملA domain - theoretic approach to computabilityon the real line 1
In recent years, there has been a considerable amount of work on using continuous domains in real analysis. Most notably are the development of the generalized Riemann integral with applications in fractal geometry, several extensions of the programming language PCF with a real number data type, and a framework and an implementation of a package for exact real number arithmetic. Based on recurs...
متن کاملPrediction of Sulfate Scale Depositions in Oilfield Operations Using Arithmetic of LR Fuzzy Numbers
In this study fuzzy arithmetic is presented as a tool to tackle the prediction of the amount of barium, strontium and calcium sulfates scales in oilfield operations. Since the shape of fuzzy numbers’ membership functions is a spread representative of the whole possible values for a special model parameter, fuzzy numbers are able to consider the uncertainties in parameter determinations and thus...
متن کاملA Multiresolution Homogenization of Modal Analysis with Application to Layered Media
We apply multiresolution techniques to study the eeective properties of boundary value problems. Conditions under which boundary values are preserved in the eeective (\homogenized") formulation are developed and discussed. Relations between the eigenfunctions and eigenvalues of the generic formulation and those of the eeective formulation are explored. Applications to the construction of eeecti...
متن کاملComputations with one and two real algebraic numbers
We present algorithmic and complexity results concerning computations with one and two real algebraic numbers, as well as real solving of univariate polynomials and bivariate polynomial systems with integer coefficients using Sturm-Habicht sequences. Our main results, in the univariate case, concern the problems of real root isolation (Th. 19) and simultaneous inequalities (Cor. 26) and in the ...
متن کامل