The iterative method to solve f(x)=0, given by the fixed-point method g(x)=x, where pn=g(pn-1)=pn-1-(f(pn-1))/(f^'(pn-1))-(f^''(pn-1))/(2 f^'(pn-1))[(f(pn-1))/(f^'(pn-1))]^2, for n=1,2,3, …has g^'(p)=g^''(p)=0. This will generally yield cubic ( α=3 ) convergence. Expand the analysis of Example 1 to compare quadratic and cubic convergence. | Numerade
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The iterative method to solve f(x)=0, given by the fixed-point method g(x)=x, where pn=g(pn-1)=pn-1-(f(pn-1))/(f^'(pn-1))-(f^''(pn-1))/(2 f^'(pn-1))[(f(pn-1))/(f^'(pn-1))]^2, for n=1,2,3,
The iterative method to solve f(x)=0, given by the fixed-point method g(x)=x, where pn=g(pn-1)=pn-1-(f(pn-1))/(f^'(pn-1))-(f^''(pn-1))/(2 f^'(pn-1))[(f(pn-1))/(f^'(pn-1))]^2, for n=1,2,3, …has g^'(p)=g^''(p)=0. This will generally yield cubic ( α=3 ) convergence. Expand the analysis of Example 1 to compare quadratic and cubic convergence.
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