A historical development of the (n+1)-point secant method

[摘要] Many finite-dimensional minimization problems and nonlinear equations can be solved using Secant Methods. In this thesis, we present a historical development of the (n + 1)-point Secant Method tracing its evolution back before Newton's Method. Many believe the Secant Method arose out of the finite difference approximation of the derivative in Newton's Method. However, historical evidence reveals that the Secant Method predated Newton's Method by more than 3000 years, and it was most commonly referred to as the Rule of Double False Position.The history of the Rule of Double False Position spans a period of several centuries and many civilizations. We describe the Rule of Double False Position and compare and contrast the Secant Method in 1-D with the Regula Falsi Method. We delineate the extension of the 1-D Secant Method to higher dimensions using two viewpoints, the linear interpolation idea and Discretized Newton Methods.

[发布机构] Rice University

[效力级别] Computer