SONGKLANAKARIN JOURNAL OF SCIENCE & TECHNOLOGY

Volume 43, No. 01, Month JANUARY, Year 2021, Pages 237 - 242

Quadratic parameter homotopy function for solving polynomial equations

Hafizudin Mohamad Nor, Siti Ainor Mohd Yatim

Abstract Download PDF

Homotopy function is used in conjunction with homotopy continuation methods (HCM) and a classical numerical method to approximate the roots of nonlinear algebraic equations, particularly in solving polynomial equations. In this paper, we develop a new function, known as quadratic parameter homotopy function, and apply it to solve several non- application equations and several application equations. This homotopy function is used in two homotopy methods i.e., Newton-HCM and Ostrowski-HCM. The results obtained indicate that the proposed homotopy function performs better than the existing homotopy functions.

Keywords

numerical method, polynomial equations, homotopy function, quadratic parameter homotopy function, homotopy method

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