Debugging Newton's Method code in two variables,

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Noob 2020-9-21

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https://ww2.mathworks.cn/matlabcentral/answers/597076-debugging-newton-s-method-code-in-two-variables

评论： Ameer Hamza 2020-9-21

采纳的回答： Ameer Hamza

在 MATLAB Online 中打开

Hi,

I wrote a simple code for Newton's Method in two variables but am having some trouble debugging it. Here's the message I get:

Index exceeds matrix dimensions.

Error in Root_finding_practice>@(x)[cos(x(2)),-x(1)*sin(x(2));x(2)*cos(x(1)),sin(x(1))]

Error in Root_finding_practice (line 34)

x(i+1) = x(i) - ( inv( J( x(i) ) ) * f( x(i) ) );

The function file code is:

function F = nonlinear_equations(x)
 
F(1) = x(1) * cos( x(2) );
 
F(2) = x(2) * sin( x(1) );
 
end

and the script file code is:

f = @(x) nonlinear_equations;
 
% Jacobian
 
J = @(x) [ cos( x(2) ), -x(1)*sin(x(2));
    x(2) * cos(x(1)), sin(x(1)) ];
 
x = [ 1, 1 ];
 
for i = 1:1000   % it should be stopped when tolerance is reached
        
    x(i+1) = x(i) - (  inv( J( x(i) ) ) * f( x(i) ) );
       
    if( abs( f( x(i+1) ) ) < 0.0001 )   % tolerance
            
            disp(double(x(i+1)));
            
            break;  
    end
       
end

What am I missing? I suspect it's the way I've defined the Jacobian anonymous function ...

Thanks,

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采纳的回答

Ameer Hamza 2020-9-21

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/597076-debugging-newton-s-method-code-in-two-variables#answer_497722

编辑：Ameer Hamza 2020-9-21

在 MATLAB Online 中打开

Check this code

f = @(x) nonlinear_equations(x);
% Jacobian
J = @(x) [cos( x(2) ), -x(1)*sin(x(2));
    x(2)*cos(x(1)), sin(x(1))];
x = [1; 1];
for i = 1:1000   % it should be stopped when tolerance is reached
    
    x(:,i+1) = x(:,i) - inv(J(x(:,i)))*f(x(:,i));
    
    if( abs(f(x(:, i+1))) < 0.0001)   % tolerance
        disp(double(x(:, i+1)));
        break;
    end
end
function F = nonlinear_equations(x)
F = zeros(2, 1);
F(1) = x(1) * cos( x(2) );
F(2) = x(2) * sin( x(1) );
end