An introduction to an ancient Chinese algorithm and its modification

An introduction to an ancient Chinese algorithm and its modification PurposeEvery 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.Design/methodology/approachAn example is given to show that the ancient Chinese algorithm is insensitive to initial guess, while a fast convergence rate is predicted.FindingsTwo new algorithms, which are suitable for numerical simulation, are introduced by absorbing the advantages of the Newton iteration method and the ancient Chinese algorithm.Research limitations/implicationsThis paper focuses on a single algebraic equation; however, it is easy to extend the theory to algebraic systems.Practical implicationsThe Newton iteration method can be updated in numerical simulation.Originality/valueThe ancient Chinese algorithm is elucidated to have modern applications in various numerical methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png international Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

An introduction to an ancient Chinese algorithm and its modification

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0961-5539
DOI
10.1108/HFF-09-2015-0377
Publisher site
See Article on Publisher Site

Abstract

PurposeEvery 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.Design/methodology/approachAn example is given to show that the ancient Chinese algorithm is insensitive to initial guess, while a fast convergence rate is predicted.FindingsTwo new algorithms, which are suitable for numerical simulation, are introduced by absorbing the advantages of the Newton iteration method and the ancient Chinese algorithm.Research limitations/implicationsThis paper focuses on a single algebraic equation; however, it is easy to extend the theory to algebraic systems.Practical implicationsThe Newton iteration method can be updated in numerical simulation.Originality/valueThe ancient Chinese algorithm is elucidated to have modern applications in various numerical methods.

Journal

international Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Nov 7, 2016

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