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• W2043938310 abstract "Recent work on Newton’s method at singularities of the Jacobian has established linear convergence under certain regularity assumptions. Here, Newton’s method is analyzed in the neighborhood of irregular singularities which include all minimizers at which the Hessian has a one-dimensional null space. Depending on a parameter specific to the underlying optimization problem or system of simultaneous equations, Newton’s method is found either to converge with a limiting ratio of about $frac{2} {3}$, or to diverge from arbitrarily close starting points, or to behave in a certain sense chaotically." @default.
• W2043938310 created "2016-06-24" @default.
• W2043938310 creator A5060495789 @default.
• W2043938310 creator A5079600875 @default.
• W2043938310 date "1983-08-01" @default.
• W2043938310 modified "2023-10-16" @default.
• W2043938310 title "Analysis of Newton’s Method at Irregular Singularities" @default.
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• W2043938310 doi "https://doi.org/10.1137/0720050" @default.
• W2043938310 hasPublicationYear "1983" @default.
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