## Iterative methods for solving nonlinear equations with finitely many roots in an interval.(English)Zbl 1247.65064

A nonlinear equation $$f(x) = 0$$ having finitely many roots in general, in a given interval, is considered. Based on the so-called numerical integration method (NIM) the author develops a new iterative method to find all of the roots. The paper is organized as follows. The first Section is preliminaries. In Section 2 a basic algorithm combining NIM and existing iterative methods for a unique simple root in an interval is studied. In the next section the method to the case of finitely many roots via partitioning the given interval is extended. In Section 4 the method for finding multiple roots by using a transformation is generalized and, additionally it is shown that it is also available to find the extrema of $$f(x)$$. The usefulness of the proposed method by performing several numerical examples is demonstrated. In the last section the method with a concluding remark is summarized.

### MSC:

 65H05 Numerical computation of solutions to single equations
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### References:

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