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

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dc.contributor.advisorTapia, Richard A.
dc.creatorPapakonstantinou, Joanna Maria
dc.date.accessioned2009-06-03T21:07:29Z
dc.date.available2009-06-03T21:07:29Z
dc.date.issued2007
dc.description.abstractMany 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.
dc.format.extent65 p.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.callnoTHESIS MATH.SCI. 2007 PAPAKONSTANTINOU
dc.identifier.citationPapakonstantinou, Joanna Maria. "A historical development of the (n+1)-point secant method." (2007) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/20568">https://hdl.handle.net/1911/20568</a>.
dc.identifier.urihttps://hdl.handle.net/1911/20568
dc.language.isoeng
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.
dc.subjectMathematics
dc.subjectComputer science
dc.titleA historical development of the (n+1)-point secant method
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematical Sciences
thesis.degree.disciplineEngineering
thesis.degree.grantorRice University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science
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