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Extension of Murakami’s high-order non-linear solver to multiple roots. (English) Zbl 1192.65052
Summary: Several one-parameter families of fourth-order methods for finding multiple zeros of non-linear functions are developed. The methods are based on T. Murakami’s fifth-order method (for simple roots) [J. Inf. Process. 1, 138–139 (1978; Zbl 0394.65015)] and they require one evaluation of the function and three evaluations of the derivative. The informational efficiency of the methods is the same as for the previously developed methods of lower order. For a double root, the method is more efficient than all previously known schemes. All these methods require the knowledge of multiplicity.

65H05 Numerical computation of solutions to single equations
65Y20 Complexity and performance of numerical algorithms
Zbl 0394.65015
Full Text: DOI
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