Advanced Methods for Solving Nonlinear Eigenvalue Problems of Generalized Phase Optimization
In the process of solving the problems of generalized phase optimization the necessity to apply an eigenvalue approach often appears. The practical statement of the optimization problems consists of using the amplitude characteristics of functions that are sought. The usual way of optimization is de...
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| Format: | Book Chapter |
| Language: | English |
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IntechOpen
2022
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| Online Access: | https://www.intechopen.com/chapters/81364 |
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| Summary: | In the process of solving the problems of generalized phase optimization the necessity to apply an eigenvalue approach often appears. The practical statement of the optimization problems consists of using the amplitude characteristics of functions that are sought. The usual way of optimization is deriving the Euler equation of the functional, which is used as criterion of optimization. As a rule, such equation is an integral one. It is worth pointing out that the integral equations of the generalized phase optimization are nonlinear ones. The characteristic property of such equations is non-uniqueness of solutions and their branching or bifurcation. The determination of branching solutions leads to the investigation of the corresponding homogeneous equations and the respective eigenvalue problem. This problem is nonlinear because of specificity of the statement of the optimization problem. The study of the above problem allows us to determine a set of points, in which the respective eigenvalues are equal to unity that determines the branching points of solutions. The data of calculations testify to the ability of the approach proposed to determine the solutions of nonlinear equations numerically with not large computations. |
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| ISBN: | 978-1-80355-822-6 |
| DOI: | 10.5772/intechopen.103948 |