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1. and the number of iterations needed to get a convergent eigenvalue have also been derived. The numerical results for the number of iterations have agreed well with the analytical results. The new power method can be used to select freely one solution of an eigenvalue problem by adjusting the parameter of the functional. Therefore, the new power method extends the application of power methods to obtain not only the dominant eigenvalue solution but also all eigen solutions. 6. Acknowledgements IWS is supported by University of Mataram through a PNBP Internal Research Grant. HS is supported by Khalifa University through a Faculty Start-Up Grant (No. 8474000351/FSU-2021-011) and a Competitive Internal Rese