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 science