How to create a vector and populate it with the first 10 roots using this Newtons method code?

Question

Diego Dranuta 2020-9-10

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https://ww2.mathworks.cn/matlabcentral/answers/591862-how-to-create-a-vector-and-populate-it-with-the-first-10-roots-using-this-newtons-method-code

回答： Alan Stevens 2020-9-11

I've created this code to calculate roots by using Newtons Method. However I only need the first 10 roots that I find with this code. I think I have to create a 10x1 matrix and populate it with the results that are not repeated. I have no idea how to do that... Any ideas? Thanks!!

syms f(x) x
f(x) = x*tan(x)-0.1; %Function 
g = diff(f);
for e=1:100 %Trying different initial guesses to get all the roots
 x(1)=e ;%initial guess
    for i=1:1000 %it should be stopped when tolerance is reached
        x(i+1) = x(i) - f(x(i))/g(x(i));%Newtons Method
        if( abs(f(x(i+1)))<0.001)   % tolerance 
          disp(double(x(i+1))); %Display result
          break;
        end
        
    end
end

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Answer 1

Alan Stevens 2020-9-11

1
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https://ww2.mathworks.cn/matlabcentral/answers/591862-how-to-create-a-vector-and-populate-it-with-the-first-10-roots-using-this-newtons-method-code#answer_492988

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Something more like this perhaps (no need for symbolic maths).

f = @(x) x.*tan(x)-0.1; %Function 
g = @(x) x.*tan(x).^2 + tan(x) + x;
tol = 0.001;  
X = zeros(10,1); % Space for 10 roots
for i = 1:10 % loop for each root in turn 
    
    err = 1;
    x = i*pi;   % initial guess
    while err>tol
        xold = x;
        x = x - f(x)/g(x);%Newtons Method
        err = abs(x - xold);
    end
    X(i) = x;
    
end
fprintf('Roots\n')
fprintf('%8.4f \n',X)