4.9 Newton's method

4.9 Newton's method - 5. Iterate until satisfied. 6.

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4.9 Newton’s Method -Finding zeros (or roots) of functions -improvement on plain linearization Y=f(x) R is a root (or zero) => f(r)=0 1. Guess x, 2. F(x1)=0? 3. Find L1(x)=F(x1)+F’(x1)(x-x1) 4. L1(x2)=F(x1)+F’(x1)(x2-x1)=0=x2=x1-f(x)/f’(x)
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Unformatted text preview: 5. Iterate until satisfied. 6. Xn=X(n-1)-F(X(n-1))/F(X(n-1)) Note: Newtons method CAN FAIL 1. F(X(n-1))=0 2. Xn or f(Xn) may diverge 3. Cycle Ex....
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4.9 Newton's method - 5. Iterate until satisfied. 6.

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