Results 1 
2 of
2
Arbitrary Precision Real Arithmetic: Design and Algorithms
, 1996
"... this article the second representation mentioned above. We first recall the main properties of computable real numbers. We deduce from one definition, among the three definitions of this notion, a representation of these numbers as sequence of finite Badic numbers and then we describe algorithms fo ..."
Abstract

Cited by 19 (0 self)
 Add to MetaCart
this article the second representation mentioned above. We first recall the main properties of computable real numbers. We deduce from one definition, among the three definitions of this notion, a representation of these numbers as sequence of finite Badic numbers and then we describe algorithms for rational operations and transcendental functions for this representation. Finally we describe briefly the prototype written in Caml. 2. Computable real numbers
Computing on Sequences of Embedded Intervals
 Reliable Computing
, 1997
"... What will prevent most users to turn from standard arithmetic to interval arithmetic is the common belief that on any reallife program, interval arithmetic will return much too pessimistic bounds to their solution. Although some adequate set of refinements usually yields satisfactory results wit ..."
Abstract
 Add to MetaCart
What will prevent most users to turn from standard arithmetic to interval arithmetic is the common belief that on any reallife program, interval arithmetic will return much too pessimistic bounds to their solution. Although some adequate set of refinements usually yields satisfactory results with interval arithmetic, an intervalnovice would most certainly not spend the time to look into the details and learn about the mathematical peculiarities of his code. We present in this work the prototype of a software library that deals almost transparently with intervals. Directly from its model of execution, the library is able to automatically decide to refine a part or the totality of an evaluation as it is needed. We also introduce a new technique based on an extended number representation that even improves the performances of the library and reduces the interval computed after a numerical evaluation. Keywords: Computer Arithmetic, Interval Arithmetic, Online Arithmetic, Red...