An optimal ball algorithm for fixed point equations

Based on a principle of successively minimizing the ball containing the solution set, a new ball algorithm is developed for solving the fixed point equation x = Tx, with T a contractive operator. It is shown that this algorithm is optimal in computational efficiency among all known ball methods for...

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Veröffentlicht in:	International journal of computer mathematics 1994-01, Vol.50 (3-4), p.183-195
Hauptverfasser:	Xu, Zongben, Shi, Xingzhong
Format:	Artikel
Sprache:	eng
Schlagworte:	Ball iteration Dahlquist constant G.1.5 Geometric estimator Region contraction algorithm
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Based on a principle of successively minimizing the ball containing the solution set, a new ball algorithm is developed for solving the fixed point equation x = Tx, with T a contractive operator. It is shown that this algorithm is optimal in computational efficiency among all known ball methods for the given problem. Numerical examples are provided to support the conclusion.
ISSN:	0020-7160 1029-0265
DOI:	10.1080/00207169408804254