How to add the count of iterations and relative error to the code?

Question

Lingbai Ren 2021-10-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1568438-how-to-add-the-count-of-iterations-and-relative-error-to-the-code

回答： Sulaymon Eshkabilov 2021-10-21

I have this Newton-Rhapson and bisection method functions, but they cannot track how mant literations operated and what the relative error is. I am wondering where I can add lines of code to let them able to achieve those?

function root = newton(fun,x0,fprime,tol,maxiter)
% newton function computes the root of the function
% fun using Newton-Raphson method
% Check whether the initial guess is a root
% Error occurs if root is not determined within the 
% desired tolerance in the max number iterations
root = x0;
iter = 0;
if ~isa(fprime, 'function_handle')
    fprime = @(x) central_difference(fun,x,1e-4);
end
while iter < maxiter
    
    if fprime(root) == x0
        disp('The derivative is equal to 0, the current root is %.2f\n',root)
        break
    end
    
    dx = -fun(root)/fprime(root);
    root = root + dx;
    
    if abs(dx) <= tol
       break 
    end
    iter = iter + 1;
end
if iter == maxiter && abs(dx) > tol
    error('root not found in given iterations')
end
end

function [c] = bisection(fun,a,b,tol,maxlits,plot_output)
% bisection function computes the root, c, of a function, fun
% initial intercal
c_old = 0;
iters = 0;
e_a_vec = [];
% While loop
while iters < maxlits
    iters = iters + 1;
    c = (a + b)/2;
    if plot_output == 1
        
        x = linspace(a,b);
        y = [];
        for i = 1:length(x)
            y(i) = fun(x(i));
        end
        
        nexttile
        hold on
        plot(a,fun(a),'-o')
        plot(b,fun(b),'-o')
        plot(c,fun(c),'-o')
        plot(x,y,'k-')
        yline(0,'--')
    end
    
    if iters >= 1
        e_a = (c - c_old)/c;
        e_a_vec(iters) = e_a;
        
        if abs(b-a)/2 < tol | abs(fun(c)) <= tol | abs(e_a) <= tol
            break
        end
        
    else abs(fun(c)) > tol
            
         error('The root is not within the desired tolerance') 
    end
    
    if fun(a) * fun(b) < 0
        
        if fun(a) * fun(c) > 0
             a = c;
        else 
             b = c;
        end
             c_old = c_old + c;
    else
        error('The limites do not bracket a root')
    end
    
end

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Answer 1

Sulaymon Eshkabilov 2021-10-21

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1568438-how-to-add-the-count-of-iterations-and-relative-error-to-the-code#answer_813223

在 MATLAB Online 中打开

Here are how you can obtain the final iteration and rel./abs error values when the roots are found.

function root = newton(fun,x0,fprime,tol,maxiter)
% newton function computes the root of the function
% fun using Newton-Raphson method
% Check whether the initial guess is a root
% Error occurs if root is not determined within the 
% desired tolerance in the max number iterations
root = x0;
iter = 0;
if ~isa(fprime, 'function_handle')
    fprime = @(x) central_difference(fun,x,1e-4);
end
while iter < maxiter
    if fprime(root) == x0
        disp('The derivative is equal to 0, the current root is %.2f\n',root)
        break
    end
    
    dx = -fun(root)/fprime(root);
    root = root + dx;
    
    if abs(dx) <= tol
        fprintf('Simulation is halted after %d iterations \n', iter)   % Number of iterations
        fprintf('Simulation is halted after %f of Rel. Error (Derivative Value) \n', dx)   % Rel. Error
        break 
    end
    iter = iter + 1;
end
if iter == maxiter && abs(dx) > tol
    error('root not found in given iterations')
end
end

function [c] = bisection(fun,a,b,tol,maxlits,plot_output)
% bisection function computes the root, c, of a function, fun
% initial intercal
c_old = 0;
iters = 0;
e_a_vec = [];
% While loop
while iters < maxlits
    iters = iters + 1;
    c = (a + b)/2;
    if plot_output == 1
        x = linspace(a,b);
        y = [];
        for i = 1:length(x)
            y(i) = fun(x(i));
        end
        
        nexttile
        hold on
        plot(a,fun(a),'-o')
        plot(b,fun(b),'-o')
        plot(c,fun(c),'-o')
        plot(x,y,'k-')
        yline(0,'--')
    end
    
    if iters >= 1
        e_a = (c - c_old)/c;
        e_a_vec(iters) = e_a;
        
        if abs(b-a)/2 < tol | abs(fun(c)) <= tol | abs(e_a) <= tol
        fprintf('Simulation is halted after %d iterations \n', iters)   % Number of iterations
        fprintf('Simulation is halted after %f of Rel Diff \n', abs(b-a)/2)  % Rel. Difference
        fprintf('Simulation is halted after %f of Abs. Fcn. Value \n', abs(fun(c)))   % Abs. Value
        fprintf('Simulation is halted after %f of Abs. Error \n', abs(e_a))   % Abs. Error
        break
        end
     else abs(fun(c)) > tol           
         error('The root is not within the desired tolerance') 
    end
        if fun(a) * fun(b) < 0
        
        if fun(a) * fun(c) > 0
             a = c;
        else 
             b = c;
        end
             c_old = c_old + c;
    else
        error('The limites do not bracket a root')
    end 
end