AbstractApproximations based on dyadic centred intervals are investigated as a means for implementing exact real arithmetic. It is shown that the field operations can be implemented on these approximations with optimal or near optimal results. Bounds for the loss in quality of approximations for each of the field operations are also given. These approximations can be used as a more efficient alternative to endpoint based implementations of interval analysis
This paper investigates an arithmetic based upon the representation of computable exact real numbers...
This paper justifies why an arbitrary precision interval arithmetic is needed: to provide accurate r...
International audienceWe describe here a representation of computable real numbers and a set of algo...
www.elsevier.com/locate/jlap Exact real arithmetic using centred intervals and bounded error term
AbstractA real number x is said to be effective if there exists an algorithm which, given a required...
Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic d...
International audienceThis paper presents a set of tools for mechanical reasoning of numerical bound...
33 pagesThe Mathemagix project aims at the development of a ''computer analysis'' system, in which n...
AbstractI discuss the design and performance issues arising in the efficient implementation of the s...
AbstractThis paper addresses the topic of the refinement of exact real numbers. It presents a three-...
In this article, we consider a simple representation for real numbers and propose top-down procedure...
"Topology optimization theory and applications toward wide fields of natural sciences". May 7～9, 201...
We consider biperiodic integral equations of the second kind with weakly singular kernels such as th...
Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of rea...
International audienceWe describe a computing method of the computable (or constructive) real number...
This paper investigates an arithmetic based upon the representation of computable exact real numbers...
This paper justifies why an arbitrary precision interval arithmetic is needed: to provide accurate r...
International audienceWe describe here a representation of computable real numbers and a set of algo...
www.elsevier.com/locate/jlap Exact real arithmetic using centred intervals and bounded error term
AbstractA real number x is said to be effective if there exists an algorithm which, given a required...
Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic d...
International audienceThis paper presents a set of tools for mechanical reasoning of numerical bound...
33 pagesThe Mathemagix project aims at the development of a ''computer analysis'' system, in which n...
AbstractI discuss the design and performance issues arising in the efficient implementation of the s...
AbstractThis paper addresses the topic of the refinement of exact real numbers. It presents a three-...
In this article, we consider a simple representation for real numbers and propose top-down procedure...
"Topology optimization theory and applications toward wide fields of natural sciences". May 7～9, 201...
We consider biperiodic integral equations of the second kind with weakly singular kernels such as th...
Interval arithmetic is arithmetic for continuous sets. Floating-point intervals are intervals of rea...
International audienceWe describe a computing method of the computable (or constructive) real number...
This paper investigates an arithmetic based upon the representation of computable exact real numbers...
This paper justifies why an arbitrary precision interval arithmetic is needed: to provide accurate r...
International audienceWe describe here a representation of computable real numbers and a set of algo...
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