High-order nonlinear solver for multiple roots. (English) Zbl 1142.65044

Summary: A method of order four for finding multiple zeros of nonlinear functions is developed. The method is based on P. Jarratt’s fifth-order method (for simple roots) [Comput. J. 8, 398–400 (1966; Zbl 0141.13404)] 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.


65H05 Numerical computation of solutions to single equations


Zbl 0141.13404


Full Text: DOI


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