On quotient-convergence factors. (English) Zbl 0880.65026
The problem
\[
y_{n+1}= \lambda\cdot y_n,\qquad y_0=x,
\]
and the recurrence
\[
x_{n+1}= \lambda\cdot x_n+\Omega x_n, \qquad x_0=x,
\]
\((n=0,1,2,\dots)\) are considered where \(x_n\), \(y_n\) belong to a certain linear space \(X\) over the field of real numbers \(\mathbb{R}\), \(\Omega\) is a linear operator on \(X\) and \(\lambda\in \mathbb{R}\) is fixed. It is expected then that the behaviour of the perturbed sequence \(\{x_n\}\) resembles that of \(\{y_n\}\).
Reviewer: Costică Moroşanu (Iaşi)
MSC:
65J10 | Numerical solutions to equations with linear operators |
47A50 | Equations and inequalities involving linear operators, with vector unknowns |
References:
[1] | Jackiewicz, Z.; Kwapisz, M.; Lo, E., Waveform relaxation methods for functional differential systems of neutral type, J. Math. Anal. Appl., 207, 255-285 (1997) · Zbl 0874.65056 |
[2] | Krasnosel’skii, M. A.; Vainikko, G. M.; Zabreiko, P. P.; Rutitskii, Ya. B.; Stetsenko, V. Ya., Approximate Solution of Operator Equations (1972), Wolters-Noordhoff: Wolters-Noordhoff Groningen · Zbl 0231.41024 |
[3] | Ortega, J. M.; Rheinboldt, W. C., Iterative Solutions of Nonlinear Equations in Several Variables (1970), Academic Press: Academic Press New York/London · Zbl 0241.65046 |
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