Introduction In this paper we present a modification of Gauss-Huard's method for solving dense linear systems that allows an efficient implementation on machines with a hierarchical memory structure. GaussHuard's method resembles Gauss-Jordan's method in the fact that it reduces the given system by elementary transformations to a diagonal system and it resembles regular Gaussian elimination in ...

This paper presents an e cient implementation of incomplete LU (ILU) factorizations that are derived from the Crout version of Gaussian elimination (GE). At step k of the elimination, the k-th row of U and the k-th column of L are computed using previously computed rows of U and columns of L. The data structure and implementation borrow from already known techniques used in developing both spar...

More recent models have attempted to use better physics to describe ice velocities in regions where velocities vary significantly over short distances. These models use a 3-dimensional, rectangular FEM grid. While the 2-dimensional model is used for an entire ice sheet, the 3-dimensional model is used over a limited area of interest with a smaller distance between grid points. Output of the 2-d...

In Gaussian elimination it is often desirable to preserve existing zeros (sparsity). This is closely related to perfect elimination schemes on graphs. Such schemes can be found in polynomial time. Gaussian elimination uses a pivot for each column, so opportunities for preserving sparsity can be missed. In this paper we consider a more flexible process that selects a pivot for each nonzero to be...

The additive attack public mutual information game is explicitly solved for one of the simplest quantization based watermarking schemes, the scalar Costa scheme (SCS). It is a zero-sum game played between the embedder and the attacker, and the payoff function is the mutual information. The solution of the game, a subgame perfect nash equilibrium, is found by backward induction. Therefore, the B...

There is a growing interest in using Kalman-filter models in brain modelling. In turn, it is of considerable importance to make Kalman-filters amenable for reinforcement learning. In the usual formulation of optimal control it is computed off-line by solving a backward recursion. In this technical note we show that slight modification of the linear-quadratic-Gaussian Kalman-filter model allows ...

Recent work by Sweet and Brent on the fast factorization of Cauchy-like matrices through a fast version of Gaussian elimination with partial pivoting has uncovered a potential stability problem which is not present in ordinary Gaussian elimination: excessive growth in the generators used to represent the matrix and its Schur complements can lead to large errors. A natural way to x this problem ...

We propose a method of solving large sparse systems of homogeneous linear equations over GF(2), the field with two elements. We modify an algorithm due to Wiedemann. A block version of the algorithm allows us to perform 32 matrix-vector operations for the cost of one. The resulting algorithm is competitive with structured Gaussian elimination in terms of time and has much lower space requiremen...