mws_gen_nle_ppt_secant(1) - Secant Method Major: All...

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1/10/2010 http://numericalmethods.eng.usf.edu 1 Secant Method Major: All Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates
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Secant Method http://numericalmethods.eng.usf.edu
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http://numericalmethods.eng.usf.edu 3 Secant Method – Derivation ) (x f ) f(x - = x x i i i i + 1 f(x) f(x i ) f(x i-1 ) x i+2 x i+1 x i X θ ( ) [ ] i i x f x , 1 1 ) ( ) ( ) ( = i i i i i x x x f x f x f ) ( ) ( ) )( ( 1 1 1 + = i i i i i i i x f x f x x x f x x Newton’s Method Approximate the derivative Substituting Equation (2) into Equation (1) gives the Secant method (1) (2) Figure 1 Geometrical illustration of the Newton-Raphson method.
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http://numericalmethods.eng.usf.edu 4 Secant Method – Derivation ) ( ) ( ) )( ( 1 1 1 + = i i i i i i i x f x f x x x f x x The Geometric Similar Triangles f(x) f(x i ) f(x i-1 ) x i+1 x i-1 x i X B C E D A 1 1 1 1 ) ( ) ( + + = i i i i i i x x x f x x x f DE DC AE AB = Figure 2 Geometrical representation of the Secant method. The secant method can also be derived from geometry: can be written as On rearranging, the secant method is given as
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http://numericalmethods.eng.usf.edu 5 Algorithm for Secant Method
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http://numericalmethods.eng.usf.edu 6 Step 1 0 10 1 1 x - x x = i i i a × + + Calculate the next estimate of the root from two initial guesses Find the absolute relative approximate error ) ( ) ( ) )( ( 1 1 1 + = i i i i i i i x f x f x x x f x x
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http://numericalmethods.eng.usf.edu
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

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mws_gen_nle_ppt_secant(1) - Secant Method Major: All...

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