RC
1998
13 years 4 months ago
1998
Interval arithmetic is based on the fact that for intervals on the real line, the element-wise product of two intervals is also an interval. This property is not always true: e.g....
CCE
2004
13 years 4 months ago
2004
The results of experimental testing of balanced random interval arithmetic with typical mathematical test functions and practical problem are presented and discussed. The possibili...
CORR
2007
Springer
13 years 4 months ago
2007
Springer
—Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a...
INFORMATICALT
2006
13 years 4 months ago
2006
New ways to estimate ranges of values of functions from standard and inner interval arithmetic have been proposed. Using the proposed ways ranges of values of mathematical test fun...
CORR
2006
Springer
13 years 4 months ago
2006
Springer
We present in this paper a library to compute with Taylor models, a technique extending interval arithmetic to reduce decorrelation and to solve differential equations. Numerical s...
COMPUTING
2006
13 years 4 months ago
2006
The idea of containment sets (csets) is due to Walster and Hansen, and the theory is mainly due to the first author. Now that floating point computation with infinities is widely a...
COMPUTING
2006
13 years 4 months ago
2006
Abstract We are dealing with the optimal, i.e. densest packings of congruent circles into the unit square. In the recent years we have built a numerically reliable, verified method...
IVCNZ
1998
13 years 5 months ago
1998
: Interval arithmetic is a method for performing computations on measurements that are only known to within a xed error range. As the measurements are combined mathematically, thei...
CGVR
2006
13 years 6 months ago
2006
In this paper, we propose a recursive Taylor method for ray-casting algebraic surfaces. The performance of this approach is compared with four other candidate approaches to raycas...
DAGSTUHL
2008
13 years 6 months ago
2008
ABSTRACT. We present an implementation of double precision interval arithmetic using the single-instruction-multiple-data SSE-2 instruction and register set extensions. The impleme...