Newtons Method, help calling anon function inside of function file

Question

Peter M Hogan 2019-2-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/445370-newtons-method-help-calling-anon-function-inside-of-function-file

评论： Walter Roberson 2019-2-18

Ok so I have been tasked with writing a file myNewton which finds the root of any function given the listed inputs. I am maybe misunderstanding how to implement the method in general, but my matlab related question pertains more to the nature of calling anony functions inside of function files. I do not do this here but I anticipate that the best way to solve this problem is to do that. I am basically confused! Any help is appreciated, here is what I have so far.

function p = myNewton(f,fprime,x0,tol)
%input f, anonymous function for root finding problem
%input fprime, anonlymous function, the derivative of f
%input x0, an initial guess
%input tol, a tolerance (method will stop when successive iterates are within tol of each other)
%output p, a root f(p) = 0
    x(1) = x0 - (f(x0)/fprime(x0));
    k = 2;
    ex(1) = abs(x(1)-x0);%error
    while (ex(k-1) >= tol) %while my error is greater than tolerance
        x(k) = x(k-1) - (f(x(k-1))/fprime(x(k-1)));
        k = k+1;
    end
end

code to call function;

%As a test, the root of f(x) = x+2^x is -0.64118574
% define f, fprime, an initial guess (you can use 1), and use a tolderance of 1e-6
% send these into the function and store the result as the variable p
format long % to display more digits
x0=1;
tol=1e-6;
myNewton('x+2^x','diff(x+2^x)',x0,tol)

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Answer 1

Walter Roberson 2019-2-17

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https://ww2.mathworks.cn/matlabcentral/answers/445370-newtons-method-help-calling-anon-function-inside-of-function-file#answer_361381

在 MATLAB Online 中打开

You are calling the anonymous function properly in your code.

Your problem is that you are not passing in an anonymous function. You are passing in character vectors.

myNewton(@(x) x+2^x, @(x) 2^x * log(2) + 1, x0, tol)

You cannot ask to diff(x+2^x) unless you have the symbolic toolbox.

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Peter M Hogan 2019-2-18

编辑：Peter M Hogan 2019-2-18

在 MATLAB Online 中打开

function p = myNewton(f,fprime,x0,tol)
%input f, anonymous function for root finding problem
%input fprime, anonlymous function, the derivative of f
%input x0, an initial guess
%input tol, a tolerance (method will stop when successive iterates are within tol of each other)
%output p, a root f(p) = 0
    x(1) = x0 - (f(x0)/fprime(x0));
    k = 2;
    ex(1) = abs(x(1)-x0);%error
    while (ex(k-1) >= tol) %while my error is greater than tolerance
        x(k) = x(k-1) - (f(x(k-1))/fprime(x(k-1)));
        k = k+1;
        ex(k)=abs(x(k)-x0);
    end
    p=x(k);
end

this is my new code. if you have any insights, i want p to express the root of the function. i am not sure where i am going wrong.

Walter Roberson 2019-2-18

Where do you assign ex(2) ?

When k = 2 you use ex(k-1) which is ex(1), which you have assigned to specifically, so that part is good. You then increment k from 2 to 3, and assign to ex(3). Your while loop then tests ex(3-1) which is ex(2) but you did not assign to ex(2)

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