Some vector sequence transformations with applications to systems of equations
- 35 Downloads
First, recursive algorithms for implementing some vector sequence transformations are given. In a particular case, these transformations are generalizations of Shanks transformation and the G-transformation. When the sequence of vectors under transformation is generated by linear fixed point iterations, Lanczos' method and the CGS are recovered respectively. In the case of a sequence generated by nonlinear fixed point iterations, a quadratically convergent method based on the ε-algorithm is recovered and a nonlinear analog of the CGS method is obtained.
Subject classificationAMS (MOS) 65B05 65F10 65F25
KeywordsVector sequence extrapolation Lanczos method
Unable to display preview. Download preview PDF.
- C. Brezinski,Accélération de la Convergence en Analyse Numerique, Lecture Notes in Mathematics vol. 584 (Springer, Berlin, 1977).Google Scholar
- C. Brezinski, Généralisations de la transformation de Shanks, de la table de Padé et de l' ε-algorithme, Calcolo 12 (1975) 317–360.Google Scholar
- C. Brezinski,Padé-type Approximation and General Orthogonal, Polynomials Birkhäuser, Basel, 1980.Google Scholar
- C. Brezinski, Some determinatal identities in a vector space, with applications, inPadé Approximation and its Applications, eds. H. Werner et al., Lecture Notes in Mathematics, vol. 1071 (Springer, Berlin, 1984).Google Scholar
- C. Brezinski and M. Redivo Zaglia, A new presentation of orthogonal polynomials with applications to their computation, Numer. Algorithms 1 (1991) 207–221.Google Scholar
- C. Brezinski and M. Redivo Zaglia,Extrapolation Methods. Theory and Practice (North-Holland, Amsterdam, 1991).Google Scholar
- C. Brezinski and H. Sadok, Lanczos type methods for systems of linear equations, submitted.Google Scholar
- H. Le Ferrand, Convergence of the topological ε-algorithm for solving systems of nonlinear equations, Numer. Algorithms, this volume.Google Scholar