The $\varepsilon $-Algorithm and Padé-Approximants in Operator Theory
Copyright policy )The $\varepsilon $-Algorithm and Padé-Approximants in Operator Theory
In a previous paper [Lect. Notes Math. 765, 61-87 (1979; Zbl 0431.41019)] the author defined rational functions approximating the formal sum of a power series in n variables, and showed that the expressions involved satisfy the relationships of the \(\epsilon\)-algorithm. This material is repeated in the present paper, and illustrations concerning the solution of nonlinear operator equations are provided.
- University of Antwerp Belgium
Banach space, Numerical solutions to equations with nonlinear operators, Equations involving nonlinear operators (general), commutative Banach algebra, multivariate power series, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Algorithms for approximation of functions, Numerical summation of series, epsilon-algorithm, Padé approximation, Padé-approximants, sequence transformation, Mathematics
Banach space, Numerical solutions to equations with nonlinear operators, Equations involving nonlinear operators (general), commutative Banach algebra, multivariate power series, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Algorithms for approximation of functions, Numerical summation of series, epsilon-algorithm, Padé approximation, Padé-approximants, sequence transformation, Mathematics
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