The Generalized Gauss Reduction Algorithm

The Generalized Gauss Reduction Algorithm

We generalize the Gauss algorithm for the reduction of two–dimensional lattices from the l2-norm to arbitrary norms and extend Vallée’s analysis [J. Algorithms 12 (1991), 556-572] to the generalized algorithm.

The Lattice Reduction Algorithm of Gauss: An Average Case Analysis

The lattice reduction algorithm of Gauss is shown to have an average case complexity which is asymptotic to a constant. Introduction. The “reduction” algorithm of Gauss plays an important r6le in several areas of computational number theory, principally in matters related to the reduction of integer lattice bases. It is also intimately connected with extensions to complex numbers of the Euclide...

Gauss elimination algorithm for interval matrix

The Fast Generalized Gauss Transform

The fast Gauss transform allows for the calculation of the sum of N Gaussians at M points in O(N + M) time. Here, we extend the algorithm to a wider class of kernels, motivated by quadrature issues that arise in using integral equation methods for solving the heat equation on moving domains. In particular, robust high-order product integration methods require convolution with O(q) distinct Gaus...

Generalized Gauss – Radau and Gauss – Lobatto Formulae ∗

Computational methods are developed for generating Gauss-type quadrature formulae having nodes of arbitrary multiplicity at one or both end points of the interval of integration. Positivity properties of the boundary weights are investigated numerically, and related conjectures are formulated. Applications are made to moment-preserving spline approximation. AMS subject classification: 65D30.