Lec11 - Lecture 11 More root finding methods method...

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Lecture 11 Rootfinding – Newton’s and secant methods 1 Lecture 11 More root finding methods Newton’s method Very fast way to find roots Requires taking the derivative of f(x) Can be unstable if ‘unattended’ Secant method Similar to Newton’s method, but derivative is numerical not analytical
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Lecture 11 Rootfinding – Newton’s and secant methods 2 Newton’s method -15 -10 -5 0 5 10 15 -10 0 5 1 2 5 . 0 18 . 0 ) ( 2 3 + - - = x x x x f
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Lecture 11 Rootfinding – Newton’s and secant methods 3 -6 -4 -2 0 2 4 6 8 10 12 3 6 7 2 54 . 0 ) ( 2 - - = x x dx x df 1 2 5 . 0 18 . 0 ) ( 2 3 + - - = x x x x f xold old old new dx x df f x x - = ) ( xold new old new old dx x df x x f f = - - ) ( Define slope: X old  = 4  f(x old ) = -3.48 df/dx@ x old  = 2.64 X old  = 5.318  f(x old ) = 3.296 df/dx@ x old  =7.955 X new  = 5.318
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Lecture 11 Rootfinding – Newton’s and secant methods 4 Newton Method Calculations xold f(xold) df/dx@xold xnew 4.00 -3.48     2.64 5.31818 5.31818 3.2967     7.95467 4.90375 4.90375 0.394565     6.08148 4.83887 4.83887 0.008993     5.80503 4.837315 4.837315 0.0000051     5.79848 4.837315 2
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This note was uploaded on 02/26/2008 for the course ENGR 1 taught by Professor X during the Spring '07 term at Lehigh University .

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Lec11 - Lecture 11 More root finding methods method...

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