Newton’s Method at Singular Points. II - Concepedia

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Newton’s Method at Singular Points. II

56

Citations

5

References

1980

Year

D. W. Decker, C. T. Kelley

SIAM Journal on Numerical Analysis

Numerical AnalysisSingular ProblemsPerturbation MethodSingularly Perturbed ProblemSufficient ConditionsSecond OrderSingular PointsConvergence Analysis

Abstract

A result giving sufficient conditions for convergence of Newton iterates is given for a class of singular problems. The singularities considered are of second order. Convergence of asymptotic linear ratio $\frac{2}{3}$ is obtained.

References

	Year	Citations
Convergence of the newton process to multiple solutions L. B. Rall Numerische Mathematik Numerical AnalysisPerturbation MethodNewton ProcessNonlinear EquationConvergence Analysis	1966	133
Applications of generic bifurcation. II Shui-Nee Chow, Jack K. Hale, John Mallet‐Paret Archive for Rational Mechanics and Analysis Dynamical AnalysisBifurcation TheoryGeneric BifurcationStability	1976	122
On Newton’s Method for Singular Problems G. W. Reddien SIAM Journal on Numerical Analysis Numerical AnalysisSpectral TheoryEngineeringSingular ProblemsPerturbation Method	1978	115
Newton’s Method at Singular Points. I D. W. Decker, C. T. Kelley SIAM Journal on Numerical Analysis Numerical AnalysisNumerical ComputationEngineeringSingular ProblemsSingularly Perturbed Problem	1980	114
Newton’s Method and the Goldstein Step-Length Rule for Constrained Minimization Problems J. C. Dunn SIAM Journal on Control and Optimization	1980	46

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