A robust Kantorovich鈥檚 theorem on the inexact Newton method with relative residual error tolerance

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• 作者：O.P. Ferreira^a ; ^{orizon@mat.ufg.br} ; B.F. Svaiter^b ; ^{benar@impa.br}
• 关键词：Kantorovich&rsquo ; s theorem ; Inexact Newton method ; Banach space
• 刊名：Journal of Complexity
• 出版年：2012
• 期刊代码：73_0885064x
• 类别：mt
• 出版时间：June, 2012
• 卷：28
• 期：3
• 页码：346-363
• 文件大小：268 K

摘要

We prove that under semi-local assumptions, the inexact Newton method with a fixed relative residual error tolerance converges -linearly to a zero of the nonlinear operator under consideration. Using this result we show that the Newton method for minimizing a self-concordant function or to find a zero of an analytic function can be implemented with a fixed relative residual error tolerance.

In the absence of errors, our analysis retrieve the classical Kantorovich Theorem on the Newton method.