lecturenotes10_6

# lecturenotes10_6 - = x^2-6*x 2 within a tolerance of 0.001...

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Newton’s Method Monday, October 6 2008

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Topics Newton’s method Review of histograms
Newton’s Method Newton’s Method is another numerical  root finding technique Under most circumstances, it converges  faster than bisection Based on the evaluation of the function  and its derivative Also an iterative technique that is easy to  program

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The Concept: x x 1 f(x 1 ) x 2 f(x 2 )
Zoomed x 2 f(x 2 ) x 3

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MiniTask Write the algorithm to use Newton’s  Method to find ONE root of the equation y

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Unformatted text preview: = x^2-6*x+2 within a tolerance of 0.001 Problems with Newton’s Method • Note that if we hit the inflection point with one of our guesses… • the slope of the tangent is infinite • the tangent line will NEVER intersect the x-axis • interates endlessly Comparing convergence with Bisection • We can run a bisection routine with the same function and compare – number of iterations – computation time...
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lecturenotes10_6 - = x^2-6*x 2 within a tolerance of 0.001...

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