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The Secant Method - USM

Jim LambersMAT 772 Fall Semester 2010-11 lecture 4 NotesThese notes correspond to Sections and in the Secant MethodOne drawback of Newton s Method is that it is necessary to evaluate ( ) at various points, whichmay not be practical for some choices of . Thesecant methodavoids this issue by using a finitedifference to approximate the derivative. As a result, ( ) is approximated by asecant linethroughtwo points on the graph of , rather than a tangent line through one point on the a Secant line is defined using two points on the graph of ( ), as opposed to a tangentline that requires information at only one point on the graph, it is necessary to choose two initialiterates 0and 1. Then, as in Newton s Method , the next iterate 2is then obtained by computingthe -value at which the Secant line passing through the points ( 0, ( 0)) and ( 1, ( 1)) has a -coordinate of zero.

Jim Lambers MAT 772 Fall Semester 2010-11 Lecture 4 Notes These notes correspond to Sections 1.5 and 1.6 in the text. The Secant Method One drawback of Newton’s method is that it is necessary to evaluate f0(x) at various points, which may not be practical for some choices of f.

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