Quadratic parameter homotopy function for solving polynomial equations

• Main Authors: Hafizudin Mohamad Nor, Siti Ainor Mohd Yatim
• Format: Article
• Language: English
• Published: Prince of Songkla University 2021-02-01
• Series: Songklanakarin Journal of Science and Technology (SJST)
• Subjects: numerical method; polynomial equations; homotopy function; quadratic parameter homotopy function; homotopy method
• Online Access: http://rdo.psu.ac.th/sjstweb/journal/43-1/31.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.