lecture20 - CMPSC/MATH 451 Numerical Computations Lecture...

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Unformatted text preview: CMPSC/MATH 451 Numerical Computations Lecture 20 October 7, 2011 Prof. Kamesh Madduri Class Overview Quadratic Interpolation Inverse Quadratic Interpolation Linear Fractional Interpolation Dekkers method, Brents method Review of all methods Exercises 2 Nonlinear Equations Numerical Methods in One Dimension Methods for Systems of Nonlinear Equations Bisection Method Fixed-Point Iteration and Newtons Method Additional Methods Higher-Degree Interpolation Secant method uses linear interpolation to approximate function whose zero is sought Higher convergence rate can be obtained by using higher-degree polynomial interpolation For example, quadratic interpolation (Mullers method) has superlinear convergence rate with r 1 . 839 Unfortunately, using higher degree polynomial also has disadvantages interpolating polynomial may not have real roots roots may not be easy to compute choice of root to use as next iterate may not be obvious Michael T. Heath Scientific Computing 32 / 55 Nonlinear Equations...
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This note was uploaded on 01/19/2012 for the course CMPSC 451 taught by Professor Staff during the Spring '08 term at Pennsylvania State University, University Park.

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lecture20 - CMPSC/MATH 451 Numerical Computations Lecture...

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