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A new family of Schröder’s method and its variants based on power means for multiple roots of nonlinear equations. (English)
Int. J. Math. Educ. Sci. Technol. 41, No. 4, 558-565 (2010).
Summary: In this article, we derive one-parameter family of Schröder’s method based on {\it K. C. Gupta} et al.’s [Int. J. Math. Educ. Sci. Technol. 40, No. 4, 571‒575 (2009; Zbl 1294.97017; ME 2009d.00536)] family of ellipse methods for the solution of nonlinear equations. Further, we introduce new families of Schröder-type methods for multiple roots with cubic convergence. Proposed families are derived from modified Newton’s method for multiple roots and one-parameter family of Schröder’s method. Numerical examples are also provided to show that these new methods are competitive to other known methods for multiple roots.
Classification: N35 N45
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