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

Simple item page
dc.contributor.advisorTapia, Richard A.en_US
dc.creatorPapakonstantinou, Joanna Mariaen_US
dc.date.accessioned2009-06-03T21:07:29Zen_US
dc.date.available2009-06-03T21:07:29Zen_US
dc.date.issued2007en_US
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.en_US
dc.format.extent65 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2007 PAPAKONSTANTINOUen_US
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>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/20568en_US
dc.language.isoengen_US
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.en_US
dc.subjectMathematicsen_US
dc.subjectComputer scienceen_US
dc.titleA historical development of the (n+1)-point secant methoden_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelMastersen_US
thesis.degree.nameMaster of Scienceen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
1442093.PDF
Size:
2.63 MB
Format:
Adobe Portable Document Format
Download
Collections
Rice University Theses and Dissertations