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Enrico M. Yambao & Ma. Carlota B. Decena
ARTICLE DOI: https://doi.org/10.53603/actamanil.65.2017.kdck3504
Iterative methods provide an alternative to finding the solutions of equations where analytical methods are inconvenient or even impossible to use. This study which focuses on cubic polynomial equation f (t) = at3 + bt2 + ct + d = 0, a > 0 with real coefficients and having an imaginary root, found that the fixed-point iteration xn+1 = h (xn) where h (t) = 1/3[f (t)/f ‘(t) –b/a] will always converge to the real part x of the imaginary root of f (t) = 0 whenever b2 – 3ac < 0. The only real root of g(t) = ½ f'(t) f ”(t) – af (t) = 0 was found to be the real part x of the imaginary root of f (t) = 0 and is always outside the interval formed by the critical numbers of the function f.
Keywords: complex roots, iteration, cubic polynomial, zero of a function
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