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Affine invariant convergence results for Newton's method (1982)

Ypma, T. J.

Springer

BIT 22 (1982), S. 108-118

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ISSN: 1572-9125

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We present a unified derivation of affine invariant convergence results for Newton's method. Initially we derive affine invariant forms of the perturbation lemma and a mean value theorem. With their aid we obtain an optimal radius of convergence for Newton's method, from which further radius of convergence estimates follow. From the Newton-Kantorovitch theorem we derive other estimates of the radius of convergence. We discuss estimation of the parameters in the expressions we have derived.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01934400

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