This dissertation focuses on a widely used linear algebra kernel to solve linear systems, that is the LU decomposition. Usually, to perform such a computation one uses the Gaussian elimination with partial pivoting (GEPP). The backward stability of GEPP depends on a quantity which is referred to as the growth factor, it is known that in general GEPP leads to modest element growth in practice. H...

We propose a systolic architecture for the triangularization via the Gauss elimination algorithm of large dense n x n matrices over GF@), where p is a prime number. The solution of large dense linear systems over GF(p) is the major computational step in various algorithms issued from arithmetic number theory and computer algebra. The proposed architecture implements the elimination with partial...

The amount of fill-in occurring in the factorization can vary from zero to complete fill, and can be controlled by specifying either the maximum level of fill LFILL, or the drop tolerance DTOL. The factorization may be modified in order to preserve row sums, and the diagonal elements may be perturbed to ensure that the preconditioner is positive-definite. Diagonal pivoting may optionally be emp...

The amount of fill-in occurring in the factorization can vary from zero to complete fill, and can be controlled by specifying either the maximum level of fill LFILL, or the drop tolerance DTOL. The factorization may be modified in order to preserve row sums, and the diagonal elements may be perturbed to ensure that the preconditioner is positive-definite. Diagonal pivoting may optionally be emp...

Cygnus X-3, among the X-ray binaries, is one of the brightest in the radio band, repeatedly exhibiting huge radio flares. The X-ray spectra shows two definite states, low (correspondingly hard) and high (correspondingly soft). During the hard state the X-ray spectra shows a pivoting behaviour correlated to the radio emission. In the high state the X-ray spectra shows a gamut of behaviour which ...

Motivated by a recent (continuous) quadratic formulation, in this paper we present a pivoting-based heuristic for graph matching based on the corresponding linear complementarity problem. Experiments are presented which demonstrate the potential of the proposed method. 2002 Elsevier Science B.V. All rights reserved.

This paper gives perturbation analyses of the Cholesky factorization with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations. The analyses more accurately reflect the sensitivity of the problem than previous such results. Both numerical results and an analysis show the standard method of symmetric pivoting usually imp...

In this paper we present a method of whole-body manipulation of large objects by a humanoid robot using a pivoting motion. Pivoting manipulation can be an alternative to pushing or lifting for more dexterous and stable operation, which is often used by humans to move large and bulky furniture. This paper describes a method and control techniques for a humanoid robot to perform the manipulation ...