Ancient chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method

Abstract

An exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2 nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.