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Historical Development of the Secant Method: From the Babylonians (18th Century BC) to Wolfe (1959 AD)

Historical Development of the Secant Method: From the Babylonians (18th Century BC) to Wolfe (1959 AD),Joanna M. Papakonstantinou,Richard A. Tapia

Historical Development of the Secant Method: From the Babylonians (18th Century BC) to Wolfe (1959 AD)  
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Many believe the Secant Method arose out of the finite difference approximation of the derivative in Newton's Method. However, historical evidencereveals that the SecantMethod predated Newton's Method by more than 3000 years. Our historical development of the Secant Method in 1-D shows it was originally referred to as the Rule of Double False Position and dates back to the Babylonians in 18th Century BC. The definition of general position is introduced, the (n + 1)-point interpolation idea is presented, and Wolfe's formulation to compute the basic (n + 1)-point secant approximation is outlined. We explain why the method is numerically unstable: it leads to ill-conditioning due to the deterioration of general positioning.
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