We describe a new LLL-type algorithm, H-LLL, that relies on Householder transformations to approximate the underlying Gram-Schmidt orthogonalizations. The latter computations are ...
In this paper, we present a new algorithm for the exact solutions of linear systems with integer coefficients using numerical methods. It terminates with the correct answer in wel...
Scalable parallel computers with TFLOPS (Trillion FLoating Point Operations Per Second) performance levels are now under construction. While we believe TFLOPS processor technology...
The IEEE P754 Draft Standard for Floating-point Arithmetic provides specifications for Decimal Floating-Point (DFP) formats and operations. Based on this standard, many developer...
Liang-Kai Wang, Charles Tsen, Michael J. Schulte, ...
Robustness problems due to the substitution of the exact computation on real numbers by the rounded floating point arithmetic are often an obstacle to obtain practical implementat...