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2016
DOI: 10.1108/hff-09-2015-0377
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An introduction to an ancient Chinese algorithm and its modification

Abstract: Purpose 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. Design/methodology/approach An example is given to show that the ancient Chinese algorithm is insensitive to initial guess, while a fast … Show more

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Cited by 52 publications
(35 citation statements)
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“…The sound will not be natural enough. If the highest normal correlation is obtained from the high-pass filtered speech signal, the position of the complex signal is marked as 1, indicating that there is a complex signal [14]. Background noise estimation: the background noise estimation is updated by the input amplitude level of the 5 Wireless Communications and Mobile Computing previous speech signal frame.…”
Section: Gsm Vad1 Algorithmmentioning
confidence: 99%
“…The sound will not be natural enough. If the highest normal correlation is obtained from the high-pass filtered speech signal, the position of the complex signal is marked as 1, indicating that there is a complex signal [14]. Background noise estimation: the background noise estimation is updated by the input amplitude level of the 5 Wireless Communications and Mobile Computing previous speech signal frame.…”
Section: Gsm Vad1 Algorithmmentioning
confidence: 99%
“…From equation ( 7), we can identify A easily by various methods (He, 2006;He and He, 2011). This paper applies Bubbfil algorithm (He, 2016), which was developed from an ancient Chinese method (He, 2006;He and He, 2011). We consider the case when k = 1 and M 0 = 1, equation ( 7) becomes:…”
Section: Taylor Seriesmentioning
confidence: 99%
“…By Bubbfil algorithm (He, 2016) as illustrated above, it is easy to solve A from equation ( 24), which is A = 0.730444669, and equation ( 23) becomes:…”
Section: High-order Approximatesmentioning
confidence: 99%
“…[20][21][22][23][24][25]29 The most important feature of a nonlinear oscillator is the relationship between frequency and amplitude, and He's frequency formula 28,29 is a simple method to estimate this relationship, which was initially inspired by an ancient Chinese algorithm. [29][30][31][32] Duffing oscillator was first proposed by Duffing in 1918 to investigate the vibration of the electromagnetic vibrating beam, 33 it can be written in the form with a damping coefficient l and a nonlinear coefficient Q: Here k is the wave number of the traveling wave. This equation seems simple but has complex dynamic behaviors.…”
Section: Introductionmentioning
confidence: 99%