Newton's forward difference table is incorrect for some Y values

Hi all,

I am doing an assessment item that requires us to construct the Newton's forward difference table for the function values Y = [y0, y1, ... yn]. The activity is on MATLAB Grader.

I keep getting the same error: "code is incorrect for some values of Y." I think I have the correct code for the table itself but I can't figure out how to make it correct for every value.

Here is my code:

function T = forward_differences(Y)
    if ~isnumeric(Y) || ~isvector(Y)    % this is my attempt to fix the error
        error('Input must be a numeric vector.');
    end
    
    n = length(Y);
    T = zeros(n,n);
    T(:,1) = Y(:);
    
    for j = 2:n
        for i = 1:n-j+1
            T(i,j) = T(i+1,j-1) - T(i,j-1);
        end
    end
end

Here is an example of output:

Y = [2 4 9]

Y = 1×3

2 4 9

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T = forward_differences(Y)

T = 3×3

2 2 3 4 5 0 9 0 0

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Thanks in advance!

[Walter Roberson]

I wonder if you need the transpose of that T -- so the first row represents the initial values, the second row represents the first differences, and so on.

[Chuguang Pan]

@Pia. You can use diff function to get different order Newton's forward difference.

Y = [2 4 9];
dY = diff(Y);
d2Y = diff(Y,2);

T = zeros(numel(Y));
 T(1,:) = Y;
 T(2,:) = paddata(dY,3);
 T(3,:) = paddata(d2Y,3);
 T

T = 3×3

2 4 9 2 5 0 3 0 0

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[Sam Chak]

Hi @Pia

The entries in Newton's forward difference table are computed as shown. While your computations appear to be correct, please verify whether the question requires you to include the column for "x" in the table as well. Occasionally, the warning messages in some grading questions are automated based on reasonable assumptions, regardless of the type of error.

https://atozmath.com/example/CONM/NumeInterPola.aspx?q=A&q1=E1