✦ LIBER ✦

Convergence Acceleration for Newton’s Method at Singular Points

✍ Scribed by Decker, D. W.; Kelley, C. T.

Book ID: 118185139
Publisher: Society for Industrial and Applied Mathematics
Year: 1982
Tongue: English
Weight: 874 KB
Volume: 19
Category: Article
ISSN: 0036-1429
DOI: 10.1137/0719012

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The classical Kantorovich theorem on Newton's method assumes that the first 5 w Ž . derivative of the operator involved satisfies a Lipschitz condition ⌫ FЈ x y 0 Ž .x5 5 5 FЈ y F L x y y . In this paper, we weaken this condition, assuming that 5 w Ž . Ž .x5 Ž5 5 . ⌫ FЈ x y FЈ x F x y x for a given