An Updated Version of the Kantorovich Theorem for Newton's Method.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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An affine invariant version of the Kantorovich theorem for Newtons method is presented. The result includes the Gragg-Tapia error bounds, as well as recent optimal and sharper upper bounds, new optimal and sharper lower bounds, and new inequalities showing q-quadratic convergence all in terms of the usual majorizing sequence. Closed form expressions for these bounds are given. Author
- Theoretical Mathematics