High-order nonlinear solver for multiple roots

Authors:
B. Neta;Anthony N. Johnson
Affiliations:
Naval Postgraduate School, Department of Applied Mathematics, Monterey, CA 93943, United States;United States Military Academy, Department of Mathematical Sciences, West Point, NY 10996, United States
Venue:
Computers & Mathematics with Applications
Year:
2008

Citing 1
Cited 9

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On the convergence radius of the modified Newton method for multiple roots under the center---Hölder condition

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Abstract

A method of order four for finding multiple zeros of nonlinear functions is developed. The method is based on Jarratt's fifth-order method (for simple roots) and it requires one evaluation of the function and three evaluations of the derivative. The informational efficiency of the method is the same as previously developed schemes of lower order. For the special case of double root, we found a family of fourth-order methods requiring one less derivative. Thus this family is more efficient than all others. All these methods require the knowledge of the multiplicity.