Need help altering code to so it records all values, not just the final ones.

Hello, I need help putting all of the i, xi, and Err values in a table with the column headers "Iteration Number", "xi", and "Error".

% 4)Use Newton Raphson's method with intial guess of 4.5 
% to find one of the roots. The stop condition is error<0.1%.
% part
%Err=relative approx error
%xi=initial guess
%y=function
%der=derivative
%i=iteration number
fprintf(' \n 4) Newton Raphsons Method \n')
fprintf(' \n a) Initial guess of 4.5 \n')
Err=1;
xi=4.5;
i=0;
while Err>.001
    y=(0.5*xi.^3)-(4*xi.^2)+(6*xi)-1;
    der=1.5*xi.^2+8*xi+6;
    xii=xi-(y/der);
    Err=abs((xii-xi)/(xii));
    xi=xii;
    i=i+1;
end
disp('Root is');
disp(xi);
disp('Relative Approximation Error');
disp(Err);

Answer 1

[Image Analyst]

To use a table, try this:

clc; % Clear the command window. close all; % Close all figures (except those of imtool.) clear; % Erase all existing variables. Or clearvars if you want. workspace; % Make sure the workspace panel is showing. format long g; format compact; fontSize = 20;

% 4)Use Newton Raphson's method with intial guess of 4.5
% to find one of the roots. The stop condition is error<0.1%.
% part
%Err=relative approx error
%xi=initial guess
%y=function
%der=derivative
%i=iteration number
fprintf(' \n 4) Newton Raphsons Method \n')
fprintf(' \n a) Initial guess of 4.5 \n')
Err=1;
xi=4.5;
i=0;
t = table(0, 0, 0, 'VariableNames', {'Iteration_Number', 'xi', 'Error'})
while Err>.001
  y=(0.5*xi.^3)-(4*xi.^2)+(6*xi)-1;
  der=1.5*xi.^2+8*xi+6;
  xii=xi-(y/der);
  Err=abs((xii-xi)/(xii));
  xi=xii;
  t{i+1, 'Iteration_Number'} = i;
  t{i+1, 'xi'} = xi;
  t{i+1, 'Error'} = Err;
  i=i+1;
end
t % Display table.
disp('Root is');
disp(xi);
disp('Relative Approximation Error');
disp(Err);

You'll see:

t =
  32×3 table
    Iteration_Number           xi                  Error        
    ________________    ________________    ____________________
     0                  4.63039723661485      0.0281611339052593
     1                  4.75460242909775      0.0261231500078256
     2                  4.87206180740243      0.0241087619467844
     3                  4.98240338473024      0.0221462552923705
     4                  5.08542318931628      0.0202578626696143
     5                  5.18106638669633      0.0184601374006014
     6                  5.26940551151001      0.0167645334223594
     7                  5.35061769927527      0.0151780957507514
     8                  5.42496239431477      0.0137041862478913
     9                   5.4927605844669      0.0123431904794569
    10                  5.55437622584841      0.0110931702996232
    11                  5.61020019850971     0.00995044217426145
    12                   5.6606368855061     0.00891007284454638
    13                  5.70609329106083     0.00796629203836284
    14                  5.74697049878916     0.00711282713856731
    15                  5.78365720623546     0.00634316767714857
    16                   5.8165250448515     0.00565076886329729
    17                  5.84592539385265     0.00502920359402285
    18                  5.87218741288532     0.00447227194674285
    19                  5.89561704494568      0.0039740763149545
    20                  5.91649677224753      0.0035290693303166
    21                  5.93508594010807      0.0031320806552974
    22                  5.95162149505599     0.00277832771483392
    23                  5.96631901188352     0.00246341451039634
    24                  5.97937390957255     0.00218332184714708
    25                  5.99096277770451     0.00193439160982435
    26                  6.00124475319516     0.00171330714101836
    27                   6.0103629022366     0.00151707129665137
    28                  6.01844557452832     0.00134298336532802
    29                  6.02560770661793     0.00118861572779571
    30                  6.03195205882755     0.00105179088754994
    31                  6.03757037616482    0.000930559312310236
Root is
          6.03757037616482
Relative Approximation Error
      0.000930559312310236