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Summary This note describes steps in the derivation of Laguerre's method for approximating the roots of a polynomial equation that are normally omitted from the few texts that discuss the method. For completeness, a proof of cubic convergence in the case of real distinct roots is given together with a number of examples.
K. A. Redish
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Some modifications of Laguerre's method
Two modifications of Laguerre's method are given. They define methods for simultaneously approximating all the zeros of a given polynomial. The asymptotic behavior of the methods is studied. The possibilities of both sequential and parallel implementations of the methods are considered.
Eskil Hansen +2 more
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Generalized Laguerre pseudospectral method based Laguerre interpolation
Applied Mathematics and Computation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Xiao-Yong, Li, Yan
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New methods of Laguerre pole optimization for the ARX model expansion on Laguerre bases
ISA Transactions, 2017The ARX-Laguerre model is a very important reduced complexity representation of linear system. However a significant reduction of this model is subject to an optimal choice of both Laguerre poles. Therefore we propose in this paper two new methods to estimate, from input/output measurements, the optimal values of Laguerre poles of the ARX-Laguerre ...
Tawfik, Najeh +4 more
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Operational methods and Laguerre–Gould Hopper polynomials
Applied Mathematics and Computation, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Khan, Subuhi, Al-Gonah, Ahmed Ali
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Laguerre Spectral Method for High Order Problems
Numerical Mathematics: Theory, Methods and Applications, 2013In this paper, we propose the Laguerre spectral method for high order problems with mixed inhomogeneous boundary conditions. It is also available for approximated solutions growing fast at infinity. The spectral accuracy is proved. Numerical results demonstrate its high effectiveness.
Zhang, Chao, Guo, Benyu, Sun, Tao
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