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ON THE CONVERGENCE RATE OF THE KRASNOSEL’SKIĬ–MANN ITERATION
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 96 / Issue 1 / August 2017
- Published online by Cambridge University Press:
- 05 January 2017, pp. 162-170
- Print publication:
- August 2017
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- Article
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The Krasnosel’skiĭ–Mann (KM) iteration is a widely used method to solve fixed point problems. This paper investigates the convergence rate for the KM iteration. We first establish a new convergence rate for the KM iteration which improves the known big-
$O$ rate to little-
$o$ without any other restrictions. The proof relies on the connection between the KM iteration and a useful technique on the convergence rate of summable sequences. Then we apply the result to give new results on convergence rates for the proximal point algorithm and the Douglas–Rachford method.
NONLINEAR ANALYSIS IN GEODESIC METRIC SPACES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 92 / Issue 3 / December 2015
- Published online by Cambridge University Press:
- 05 August 2015, pp. 514-515
- Print publication:
- December 2015
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