Display data in a while loop as a table

Hello, I'm trying to approximate the root of a function using Newton's method and display the results as a table. I've found my results but am having trouble displaying the table appropriately. I have a function file, and a script. This is my code:

Function:

function x = newtonimproved_4_7(f,df,x0,tol)
    x=x0; y=f(x); n=0;
    while abs(y)>tol
        n=n+1;
        x=x-y/df(x);
        y=f(x);
        t=table(n',x',y');
        header={'n','x_n','f(x_n)'};
        t.Properties.VariableNames=header;
        disp(t)
    end
    

Script:

clear, clc
format longg

f=@(x) x^3-5; df=@(x) 3*x^2;
newtonimproved_4_7(f,df,1,0.00001);

Also, if I can decompose all of it into just a script file and perhaps use syms instead, that'd be great, but that's not the main premise of this question.

Thanks.

[ScottB]

I don't have MATLAB in front of me at the moment but it seems that you should define a table before the loop and add entries to it in the loop then display the table after the loop has completed and you have reached the defined tolerance.

I think the current code is repeatedly defining a table with one set of entries, displaying that table then overwriting it in the next interation of the loop.

Answer 1

[Steven Lord]

Rather than building a new table each time, I'd create one before your loop and add to it then display it at the end.

f=@(x) x^3-5; df=@(x) 3*x^2;
newtonimproved_4_7(f,df,1,0.00001);

    n     x_n        f(x_n)  
    _    ______    __________

    1    2.3333        7.7037
    2    1.8617        1.4523
    3     1.722       0.10624
    4    1.7101    0.00073505
    5      1.71    3.6014e-08

function x = newtonimproved_4_7(f,df,x0,tol)
    x=x0; y=f(x); n=0;
    header={'n','x_n','f(x_n)'};
    t = table('Size', [0 3], ...
        'VariableTypes', ["double", "double", "double"], ...
        'VariableNames', header);
    while abs(y)>tol
        n=n+1;
        x=x-y/df(x);
        y=f(x);
        t(end+1, :) = {n, x, y};
    end
    disp(t)
end    

Answer 2

[Torsten]

clear, clc
format longg
f=@(x) x^3-5; df=@(x) 3*x^2;
[n,X,Y] = newtonimproved_4_7(f,df,1,0.00001);
t=table((1:n).',X',Y');
header={'n','x_n','f(x_n)'};
t.Properties.VariableNames=header;
disp(t)

    n          x_n                  f(x_n)       
    _    ________________    ____________________

    1    2.33333333333333         7.7037037037037
    2    1.86167800453515        1.45228738979579
    3    1.72200188005861       0.106235772741379
    4    1.71005973660029    0.000735045685184232
    5    1.70997595078219      3.601359477301e-08

function [n,X,Y] = newtonimproved_4_7(f,df,x0,tol)
    x=x0; y=f(x); n=0;
    X(1) = x; Y(1) = y;
    while abs(y)>tol
        n=n+1;
        x=x-y/df(x);
        y=f(x);
        X(n) = x;
        Y(n) = y;        
    end
end