**5. Conclusions**

In this paper, we presented a new one-point family of iterative methods with quadratic convergence for computing multiple roots with known multiplicity, based on the weight function technique. Analysis of the convergence showed the second order of convergence under some suppositions regarding the nonlinear function whose zeros are to be obtained. Some efficient and simple cases of the class were presented, and their stability was tested by analyzing complex geometry using a graphical tool—namely, the basin of attraction. The methods were employed to solve some real-world problems, such as the Eigenvalue problem, beam positioning problem, and the Van dar Waal equation of state, and were also compared with existing methods. Numerical comparison of the results revealed that the presented methods had good convergence behavior, similar to the well-known modified Newton's method.

**Author Contributions:** The contribution of all the authors have been similar. All of them worked together to develop the present manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** We would like to express our gratitude to the anonymous reviewers for their help with the publication of this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
