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This paper is made up of two general ideas. The rst is to extend the theory of general linear extrapolation methods to a non-commutative eld (or even a non-commutative unitary ring). The second one, by exploiting these new results, is to solve an old conjecture about Wynn's vector "-algorithm. Thus, thanks to the use of designants and Cliiord algebras, we… (More)

- C Brezinski, A Salam
- 1995

Sequence transformations are extrapolation methods. They are used for the purpose of convergence acceleration. In the scalar case, such algorithms can be obtained by two diierent approaches which are equivalent. The rst one is an elimination approach based on the solution of a system of linear equations and it makes use of determinants. The second approach… (More)

- A. SALAM
- 2011

Efficient, backward-stable, doubly structure-preserving algorithms for the Hamil-tonian symmetric and skew-symmetric eigenvalue problems are developed. Numerical experiments confirm the theoretical properties of the algorithms. Also developed are doubly structure-preserving Lanczos processes for Hamiltonian symmetric and skew-symmetric matrices.

- A. SALAM
- 2011

Efficient, backward-stable, doubly structure-preserving algorithms for the Hamil-tonian symmetric and skew-symmetric eigenvalue problems are developed. Numerical experiments confirm the theoretical properties of the algorithms. Also developed are doubly structure-preserving Lanczos processes for Hamiltonian symmetric and skew-symmetric matrices. 1.… (More)

- A. Salam
- 2011

The symplectic Gram-Schmidt (SGS) orthogonalization process is a cru-tial procedure for some important structure-preserving methods in linear algebra. The algorithm perfoms a factorization A = SR, where the ordered columns of the matrix S form a symplectic basis of the range of A, and R is J-upper triangular. There exist two versions of SGS, the classical… (More)