Iteration of a formula

Question

Sam Thorpe 2019-2-28

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评论： Sam Thorpe 2019-3-1

I have the following function y=4*(1-cos(x)).^2+x.^3. Using newtonian iteration how can iterate the formula 100 times with initial guess of x=4?

I have the following code so far which gets me the first root, but im not sure how to progress from here.

maxIter=100'; %number of iterations
x=4; %initial guess
i=0;
f=4*(1-cos(x)).^2+x.^3 %function
dfx=3*x.^2+8*sin(x)*(1-cos(x)) %derivative of function
y=x-(f/dfx) 
newx=y
x=newx
i=i+1

Thanks for any help

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Answer 1

Yasasvi Harish Kumar 2019-3-1

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Hi,

All you need is a loop. This should fix your problem.

maxIter=100'; %number of iterations
i = 1;
x(i)=4; %initial guess
while i<=maxIter
    f=4*(1-cos(x(i))).^2+x.^3 %function
    dfx=3*x(i)^2+8*sin(x(i))*(1-cos(x(i))) %derivative of function
    y=x(i)-(f/dfx) 
    i=i+1
    x(i) = y;
end