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In: Civil Engineering

Using Matlab, create a code that determines the highest real root of f(x)=x3-6x2+11x-6.1 using the Newton-Raphson...

Using Matlab, create a code that determines the highest real root of f(x)=x3-6x2+11x-6.1 using the Newton-Raphson method with x0=3.5 for three iterations. Verify that the process is quadratically convergent.

I found the code to get the highest real root (root for three iterations = 3.0473), however, I do not know how to verify that it is quadratically convergent.

Expert Solution

Convergence of Newton-Raphson method:

Suppose is a root of and is an estimate of s.t. . Then by Taylor series expansion we have,

for some between and .
By Newton-Raphson method, we know that

i.e.

Using(2*) in (1*) we get

Say

where denote the error in the solution at n and (n+1) iterations.

Newton Raphson Method is said to have quadratic convergence.

Ally Wells answered 9 months ago

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