AbstractWe extend the concept of significant digits by allowing the truncation of both the rightmost and the leftmost digits of the binary values in the computations whose output is known to be bracketted in a certain interval. This enables us to decrease the precision of some customary computations in linear algebra
Une arithmétique sûre et efficace est un élément clé pour exécuter des calculs rapides et sûrs. Le c...
AbstractArithmetic systems such as those based on IEEE standards currently make no attempt to track ...
The classical algorithm for multiple-precision division normalizes digits during each step and s...
AbstractThe aim of this work is to decrease the bit precision required in computations without affec...
The largest dense linear systems that are being solved today are of order $n = 10^7$. Single precis...
In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers ...
Today's floating-point arithmetic landscape is broader than ever. While scientific computing has tra...
In the design of digital signal processing systems, where single-precision results are required, the...
AbstractThe numbers of bit operations (bt) required for matrix multiplication (MM), matrix inversion...
All arithmetic operations can be decomposed into an infinitely accurate calculation and a subsequent...
International audienceIn this paper we treat the case of some fundamental interval matrix operations...
In this paper we present the theoretical foundation of forward error analysis of numerical algorithm...
Invited paper - MACIS 2015 (Sixth International Conference on Mathematical Aspects of Computer and I...
Floating-point arithmetic is an approximation of real arithmetic in which each operation may introdu...
International audienceWe explicit the link between the computer arithmetic problem of providing corr...
Une arithmétique sûre et efficace est un élément clé pour exécuter des calculs rapides et sûrs. Le c...
AbstractArithmetic systems such as those based on IEEE standards currently make no attempt to track ...
The classical algorithm for multiple-precision division normalizes digits during each step and s...
AbstractThe aim of this work is to decrease the bit precision required in computations without affec...
The largest dense linear systems that are being solved today are of order $n = 10^7$. Single precis...
In our recent work on iterative computation in hardware, we showed that arbitrary-precision solvers ...
Today's floating-point arithmetic landscape is broader than ever. While scientific computing has tra...
In the design of digital signal processing systems, where single-precision results are required, the...
AbstractThe numbers of bit operations (bt) required for matrix multiplication (MM), matrix inversion...
All arithmetic operations can be decomposed into an infinitely accurate calculation and a subsequent...
International audienceIn this paper we treat the case of some fundamental interval matrix operations...
In this paper we present the theoretical foundation of forward error analysis of numerical algorithm...
Invited paper - MACIS 2015 (Sixth International Conference on Mathematical Aspects of Computer and I...
Floating-point arithmetic is an approximation of real arithmetic in which each operation may introdu...
International audienceWe explicit the link between the computer arithmetic problem of providing corr...
Une arithmétique sûre et efficace est un élément clé pour exécuter des calculs rapides et sûrs. Le c...
AbstractArithmetic systems such as those based on IEEE standards currently make no attempt to track ...
The classical algorithm for multiple-precision division normalizes digits during each step and s...
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