Cálculo de Autovalores via Métodos tipo Newton
DOI:
https://doi.org/10.5540/tema.2004.05.01.0037Abstract
Neste trabalho, desenvolve-se uma análise numérica de alguns métodos de decomposição parcial do espectro de uma matriz, mostrando a relação desses métodos com o método de Newton para calcular zeros de funções. Um desses métodos é o DPSE (Dominant Pole Spectrum Eigensolver), que surgiu em problemas de Controle. Provamos nesse trabalho que esse método, que é tipo Newton, tem convergência local quadrática. São mostrados alguns resultados interessantes obtidos da aplicação do DPSE ao problema de estabilidade local do sistema elétrico de potência brasileiro, que são então comparados a resultados obtidos com métodos tradicionais utilizados também na resolução desse problema.References
[1] R. Bellman, “Introduction to Matrix Analysis”, 2nd ed., SIAM, Philadelphia, 1997.
L.H. Bezerra e C. Tomei, Spectral Transformation Algorithms for Computing Unstable Modes, Comp. Appl. Math., 18 (1999), 1-14.
L.H. Bezerra, C. Tomei e R.A. McCoy, M¨obius Transforms and Solvers for Large Sparse Generalized Nonsymmetric Eigenvalue Problems, Tech. Rep. TR/PA/98/03, CERFACS, Toulouse, 1998.
S. Gomes Jr., N. Martins e C. Portela, Computing Small-Signal Stability Boundaries for Large-Scale Power Systems, IEEE Trans. on Power Systems, 18, No. 2 (2003), 747-752.
A. Jennings e W.J. Stewart, Simultaneous Iteration for Partial Eigensolution of Real Matrices, J. Inst. Math. Appl., 15 (1975), 351–361.
R.B. Lehoucq, D.C. Sorensen e C. Yang, “ARPACK Users’ Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods”, SIAM, Philadelphia, 1998.
N. Martins, The Dominant Pole Spectrum Eigensolver, IEEE Trans. on Power Systems, 12, No. 1 (1997), 245-254.
N. Martins, L.T.G. Lima e H.J.C.P. Pinto, Computing Dominant Poles of Very High Order Transfer Functions, IEEE Trans. on Power Systems, 11, No. 1 (1996), 162-170.
N. Martins e P.E.M. Quintão, Computing dominant poles of power system multivariable transfer functions, IEEE Trans. on Power Systems, 18, No. 1 (2003), 152-159.
G. Peters e J.H. Wilkinson, Inverse Iteration, Ill-Conditioned Equations and Newton’s Method, SIAM Rev., 21 (1979), 339-360.
G.L.G. Sleijpen e H.A. Van der Vorst, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM Rev., 42 (2000), 267–293.
G.L.G. Sleijpen e H.A. Van der Vorst, The Jacobi-Davidson method for eigenvalue problems and its relation with accelerated inexact Newton schemes, em “Iterative Methods in Linear Algebra, II” (S.D. Margenov e P.S. Vassilevski, eds.), IMACS Ser. Comput. Appl. Math., 3, New Brunswick, NJ, (1996) 377-389.
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