Every student knows Newton’s iteration method from a textbook, which is widely used in numerical simulation, what few may know is that its ancient Chinese partner, Ying Buzu Shu, in about second century BC has much advantages over Newton’s method. The purpose of this paper is to introduce the ancient Chinese algorithm and its modifications for numerical simulation.
An example is given to show that the ancient Chinese algorithm is insensitive to initial guess, while a fast convergence rate is predicted.
Two new algorithms, which are suitable for numerical simulation, are introduced by absorbing the advantages of the Newton iteration method and the ancient Chinese algorithm.
This paper focuses on a single algebraic equation; however, it is easy to extend the theory to algebraic systems.
The Newton iteration method can be updated in numerical simulation.
The ancient Chinese algorithm is elucidated to have modern applications in various numerical methods.
The work is supported by Bubbfil foundation under No. Bubbfil 2014-01 for biometric design of nanofiber membranes.
He, C. (2016), "An introduction to an ancient Chinese algorithm and its modification", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 8, pp. 2486-2491. https://doi.org/10.1108/HFF-09-2015-0377Download as .RIS
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