ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

15. Numerical Analysis and Scientific Computing

Analysis, Cluj-Napoca, Romania 1991 MS Classification: 65 Cǎtinaş, Emil, ’T. Popoviciu’ Institute of Numerical Analysis, Cluj-Napoca, Romania Some semilocal convergence theorems for Newton- and Chebyshev-like methods with applications to eigenproblems Given F : ℝ^{n} → ℝ^{n}, we study some iterative methods for approximating a solution of F (x) = 0 in the assumption that the derivatives of order higher than 3 of F are the null multilinear operators. We obtain some semilocal convergence theorems which can be applied for approximating an eigenpair (v, λ) of a matrix A. Some numerical examples are provided. These results constitute joint work with I. Pǎvǎloiu. Reference. E. Cǎtinaş, I. Pǎvǎloiu, On Approximating the Eigenvalues and Eigenvectors of Linear Continuous Operators, Revue d’Analyse Numérique et de Théorie de l’Approximation, 26 (1997) no.1-2, pp.19–27.