Keywords:-

Keywords: Nonlinear Spectral Problem, Bilateral Approximations, Matrix Determinant Derivatives.

Article Content:-

Abstract

Methods and algorithms that form a one-parameter family of methods of bilateral approximations to the eigenvalues of nonlinear spectral problems are constructed. Their convergence is proved. Numerical results are given.

References:-

References

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Podlevs'kyi B. M. Bilateral Analog of the Newton Method for Determination of Eigenvalues of Nonlinear Spectral Problems. J. Math. Sci. 2009: 160: 357-367. https://doi.org/10.1007/s10958-009-9503-2.

Podlevskyi B. M. Bilateral Methods for Solving of Nonlinear Spectral Problems, Nauk dumka, Kyiv, 2014. (in Ukrainian).

Podlevskyi B. One Approach to Construction of Bilateral Approximations Methods for Solution of Nonlinear Eigenvalue Problems. American Journal of Computational Mathematics. 2012:2: 118-124. https://doi.org/10.4236/ajcm.2012.22016.

Kartyshov S. V. Numerical method for solving the eigenvalue problem for sparse matrices depending non-linearly on a spectral parameter. Comput. Math. Math. Phys. 1989: 29: 209–213. https://doi.org/10.1016/S0041-5553(89)80032-1

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Podlevskyi, B. (2020). On a Family of Newton-Like Methods for Bilateral Approximation of the Eigenvalues of Nonlinear Spectral Problems. International Journal Of Mathematics And Computer Research, 8(08), 2124-2129. https://doi.org/10.47191/ijmcr/v8i8.03