Calculs de complexité relatifs à une méthode de dissection emboîtée.
Chipman pseudoinverse of matrix, its computation and application in spline theory
Cholesky-like factorizations of skew-symmetric matrices.
Computation of determinants and inverses of rectangular or singular matrices using residue arithmetic.
Computing and Visualizing Solution Sets of Interval Linear Systems
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006The computation of the exact solution set of an interval linear system is a nontrivial task [2, 13]. Even in two and three dimensions a lot of work has to be done. We demonstrate two different realizations. The first approach (see [16]) is based on Java, Java3D, and the BigRational package [21]. An applet allows modifications of the matrix coefficients and/or the coefficients...
Convergence of Rump's method for computing the Moore-Penrose inverse
We extend Rump's verified method (S. Oishi, K. Tanabe, T. Ogita, S. M. Rump (2007)) for computing the inverse of extremely ill-conditioned square matrices to computing the Moore-Penrose inverse of extremely ill-conditioned rectangular matrices with full column (row) rank. We establish the convergence of our numerical verified method for computing the Moore-Penrose inverse. We also discuss the rank-deficient case and test some ill-conditioned examples. We provide our Matlab codes for computing the...
Counting determinants of Fibonacci-Hessenberg matrices using LU factorizations.
Criteria for Positive Definiteness of Some Band Matrices.
Crout versions of ILU factorization with pivoting for sparse symmetric matrices.