Complex symmetric systems do not in general admit a Cholesky factorization without pivoting, as would be the case for hermitian systems. Nevertheless, for some complex symmetric systems, as those coming from the discretization of boundary integral formulations, pivoting can be avoided. We present a Cholesky factorization algorithm for such complex symmetric systems. We propose a LAPACK-style im...

We present new, e cient algorithms for some fundamental computations with nite dimensional (but not necessarily commutative) associative algebras over nite elds. For a semisimple algebra A we show how to compute a complete Wedderburn decomposition of A as a direct sum of simple algebras, an isomorphism between each simple component and a full matrix algebra, and a basis for the centre of A. If ...

Given a sparse symmetric positive definite matrix AAT and an associated sparse Cholesky factorization LDLT or LLT, we develop sparse techniques for obtaining the new factorization associated with either adding a column to A or deleting a column from A. Our techniques are based on an analysis and manipulation of the underlying graph structure and on ideas of Gill et al. [Math. Comp., 28 (1974), ...

In this paper we describe new parallel cyclic wavefront algo rithms for solving the semide nite discrete time Lyapunov equation for the Cholesky factor using Hammarling s method by the message passing para digm These algorithms are based on previous cyclic and modi ed cyclic algorithms designed for the parallel solution of triangular linear systems The experimental results obtained on an SGI Po...

This paper gives perturbation analyses for the Cholesky factorization A = R T R of a real symmetric positive deenite matrix A, with the form of perturbations we could expect from the equivalent backward error in A resulting from numerically stable computations on nite precision oating point computers. First-order and rigorous perturbation bounds are are obtained. The analyses more accurately re...

Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regularization. This paper proposes a new PCD algorithm by tuning Cross Approximation (CA) algorithm to kernel matrices which merges the merits of PCD and CA, and proves as well as numerically exemplifies that it solves large ...

Basic Linear Algebra Subroutines (BLAS-3) [Cho 92] are the building block to solve a lot of numerical problems (Cholesky factorization, Gram-Schmidt ortonormalization, LU decomposition,...). Their efficient implementation on a given parallel machine is a key issue for the maximal exploitation of the system computational power. In this work we refer to a massively parallel processing SIMD machin...

Not nal version! Abstract: Starting from an algebraic equivalent of the Velte decomposition of the function space (H 1 0) n (where n = 2;3) into three orthogonal subspaces, we consider nite diierence and nite element classes for the approximate solution of the rst-kind Stokes problem in two and three dimensions which admit discrete Velte decompositions. The discrete Velte decomposition should b...

A globally consistent solution to the simultaneous localization and mapping (SLAM) problem in 2D with three degrees of freedom (DoF) poses was presented by Lu and Milios [20]. To create maps suitable for natural environments it is however necessary to consider the 6 DoF case, namely the three Cartesian coordinates and the roll, pitch and yaw angles. This article describes the extension of the p...

The scenarization of educational activities, especially those that are going to take place within e-learning platforms, has for a number of years represented a major challenge for groups working to favor the emergence of educational standards. This paper presents LDL (Learning Design Language), a meta-model proposed to formalize scenarized activities. We particularly highlight the correct adapt...