Combined Use of Monte Carlo Approach and Newton’s Method for Finding the Roots of a Characteristic Polynomial

Proceedings of the 8th International Scientific Symposium on Electrical Power Engineering "Elektroenergetika 2015" 2015
Georgi Georgiev, Igor Kryuchkov, Inga Zicmane, Sergejs Kovaļenko

This paper develops the application of Monte Carlo approach for random search algorithm to finding one of the complex roots of a characteristic polynomial (ChP) with real coefficients. The search is produced on the basis of random numbers with uniform distribution in rather narrow bounded area of the complex plane (the II quadrant). If high precision is necessary then the best random hit is used as good initial estimate for further specification of the root by the iterative Newton’s method for two equations with two unknowns (a Jacobian matrix 2х2). After finding the next root the ChP is deflated and the procedure repeats again. The specified technique is very easily and simply realized in the environment of MS Excel or MATLAB functions with the good graphic visualization which is useful in the educational process and researches at minimum computing resource. Irrespective of the high degree of ChP it is possible to direct the search process so that to find at once only those roots what are more strongly connected with instability of the electrical system. The offered algorithm allows creating effective software products.

Keywords
Monte Carlo; characteristic polynomial; complex root; random search; stability
Hyperlink
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Georgiev, G., Kryuchkov, I., Zicmane, I., Kovaļenko, S. Combined Use of Monte Carlo Approach and Newton’s Method for Finding the Roots of a Characteristic Polynomial. In: Proceedings of the 8th International Scientific Symposium on Electrical Power Engineering "Elektroenergetika 2015", Slovakia, Stará Lesná, 16-18 September, 2015. Košice: Technical University of Košice, 2015, pp.53-56. ISBN 978-80-553-2187-5.

Publication language
English (en)