Affine invariant convergence results for Newton's method |
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Authors: | T J Ypma |
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Institution: | (1) Department of Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, 2001 Johannesburg, South Africa |
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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. |
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