Antic, Dragan

Dankovic, Bratislav

Dimitrijevic, Sasa

Dimitrijevic Sasa

Dankovic Bratislav

Antic Dragan

University of Szeged

Simulation Approach for Localizing Roots of Real Coefficients Complex EquationSasa Dimitrijevic, Bratislav Dankovic, and Dragan AnticThis paper presents a new approach for solving real coefficients complex equation based on simula-tion. The procedure is used for n-th order complex equation, in the form:fz  anzn  an zn   az  a  (1)where ai  i     n are real coefficients, n is equation order and z  x iy is a complex variable.The technique relates solving complex equation:fx iy   (2)what can be written in the form:Reffx iy  g iImffx iy  g   (3)The condition (3) is fulfilled if both absolute values of real and imaginary part are equal to zero:j Reffx iyg j  j Imffx iyg j  (4)Considering that this approach is used for localization of equation (1) roots, equation (4) model willbe:  minxyj Reffx iyg j  j Imffx iyg j (5)The x, y values which correspond to minimum will be the roots of equation (1).Simulation is conducted using block diagram simulation languages (SIMULINK, etc.) where x time and as a result of simulation value  for y  y   const is obtained.  minyminxj Reffx iyg j  j Imffx iyg j (6)Repeated simulations for different values of y  y   const are performed using MATLAB pro-gramming. When the desired accuracy is accomplished, the obtained values x  x   y  y  , willrepresent one of the equation (1) roots. The procedure is then repeated for different values y  y . Inthat manner, all other roots can be localized.References[1] Karayanakis N. M., Computer-Assisted Simulation of Dynamic Systems with Block Diagram Lan-guages, CRC Press, Boca Raton, 1993.[2] Murray-Smith D. J., Continuous System Simulation, Chapman & Hall, London, 1995.[3] Kuo F. F. ed., Computer Simulation of Dynamic Systems, Prentice-Hall, New Jersey, 1972.

Simulation approach for localizing roots of real coefficients complex equation : [abstract]

http://acta.bibl.u-szeged.hu/59518/1/cscs_1998_035.pdf

Simulation approach for localizing roots of real coefficients complex equation

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