Newton's Divided Differences Function

Question

Abiageal 2024-1-25

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2074106-newton-s-divided-differences-function

编辑： Mann Baidi 2024-1-25

I am trying to make a simple code to compute newtons divided differences from an array of x values and an array of y values. I am new to coding so I am not sure if I am doing this right / where my error is and I keep getting a matrix of all zeros as my answer. Here is my coded attached below

function [B] = dividediffs(x,y)

%DIVIDEDDIFFS computes the divided differences of an array of (x,y) points

% INPUT: two arrays of x and corresponding y values OUTPUT: divided differences

n = length(x);

B = zeros(n,n);

if n == 1

B = y(1);

else

for k = 2:n

for i = 1: n-k+1

if (i+k) <= n

B(i,k) = (B(i+1,k-1)-B(i,k-1))/(x(i+k)-x(i));

end

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Answer 1

Mann Baidi 2024-1-25

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2074106-newton-s-divided-differences-function#answer_1397021

编辑：Mann Baidi 2024-1-25

在 MATLAB Online 中打开

Hi Abiageal,

As per the information provided in the question, I understand that you are facing issues in implementing 'Newton's Divided Differences Function' as you are getting 'B' a matrix of all zeros.

This is because in the 'Newton's Divided Differences Function' we need to initialize the first row of 'divided differences table'.

You can try initialising the first row with the help of this code.

x=1:10;
y= 11:20;
ans=dividediffs(x,y)
ans = 10×10
   11.0000    0.5000         0         0         0         0         0         0         0         0
   12.0000    0.5000         0         0         0         0         0         0         0         0
   13.0000    0.5000         0         0         0         0         0         0         0         0
   14.0000    0.5000         0         0         0         0         0         0         0         0
   15.0000    0.5000         0         0         0         0         0         0         0         0
   16.0000    0.5000         0         0         0         0         0         0         0         0
   17.0000    0.5000         0         0         0         0         0         0         0         0
   18.0000    0.5000         0         0         0         0         0         0         0         0
   19.0000         0         0         0         0         0         0         0         0         0
   20.0000         0         0         0         0         0         0         0         0         0
function [B] = dividediffs(x,y)
%DIVIDEDDIFFS computes the divided differences of an array of (x,y) points
%   INPUT: two arrays of x and corresponding y values OUTPUT: divided differences
n = length(x);
B = zeros(n,n);
B(:, 1) = y';
if n == 1
    B = y(1);
else
    for k = 2:n
        for i = 1: n-k+1
            if (i+k) <= n
                B(i,k) = (B(i+1,k-1)-B(i,k-1))/(x(i+k)-x(i));
            end
        end
    end
end
end