In this paper we extend some results on the factorization of matrices associated to Lucas, Pascal, Stirling sequences by the Fibonacci matrix. We provide explicit factorizations of any matrix by the matrix associated with an r-order recurrent sequence Un (having U0 = 0). The Cholesky factorization for the symmetric matrix associated to Un is also obtained.

For symmetric indeenite tridiagonal matrices, block LDL T factorization without interchanges is shown to have excellent numerical stability when a pivoting strategy of Bunch is used to choose the dimension (1 or 2) of the pivots.

We describe pPCx, a parallel variant of the PCx interior-point code for linear programming. We outline the major computational operation|parallel multifrontal Cholesky factorization|and present computational results on the IBM-SP multipro-cessor.

Let K be a symmetric indefinite matrix. Suppose that K 1⁄4 LJL is the generalized Cholesky factorization of K. In this paper we present perturbation analysis for the generalized Cholesky factorization. We obtain the first-order bound on the norm of the perturbation in the generalized Cholesky factor. Also, we give rigorous perturbation bounds. 2002 Elsevier Inc. All rights reserved.

The aim of this article is to illustrate, on the Dwork hypersurfaces xn1+· · ·+x n n−nψx1 . . . xn = 0 (with n an integer ≥ 3 and ψ ∈ F∗ q a parameter satisfying ψ n 6= 1), how the study of the representation of a finite group of automorphisms of a hypersurface in its etale cohomology allows to factor its zeta function.

In this paper we present a simpliied proof for the convergence of the windowed Cholesky factori-sation of the time{varying asynchronous CDMA channel.