Question

this is the function in matlab

function [yint] = Newtint(x, y, xx)
n= length(x);
if length(y) ~=n , error('x and y must be same length');
end
b= zeros(n,n);
b(:,1) = y(:);
  
%{
b(1,2)=b(2,1)-b(1,1)/x(2)-x(1)
  
%}
for j= 2:n
for i= 1:n-j+1
b(i, j) = (b (i+1, j-1)-b(i, j-1))/(x(i+j-1)-x(i));
end
end
xt = 1;
yint = b (1,1);
for j = 1:n-1
xt = xt* (xx-x(j));
yint = yint+b(1, j+1) *xt;
end   

end

this is the input:

>> x = [1 4 6 5]';
>> y = log(x);
>> xx=2

>> yint(x,y,xx)

this is output:

ans =

0.6288

-----------------------------------------------------

Question:

Follow the
for j= 2:n
for i= 1:n-j+1
b(i, j) = (b (i+1, j-1)-b(i, j-1))/(x(i+j-1)-x(i));
end
end

and write it step step for end
like this

step 1:
j=2 ,i=1
b(1,2)=b(2,1)-b(1,1)/x(2)-x(1)

step2 :

.....

Answer 1

Considering the value of n is 4 from the input data the steps are as follows:

Step 1:

j=2,i=1

b(1,2)=(b (2, 1)-b(1, 1))/(x(2)-x(1))

Step 2:

j=2,i=2

b(2,2)=(b (3, 1)-b(2, 1))/(x(4)-x(2))

Step 3:

j=2,i=3

b(3,2)=(b (4, 1)-b(3, 1))/(x(4)-x(3))

Step 4:

j=3,i=1

b(1,3)=(b (2, 2)-b(1, 2))/(x(3)-x(1))

Step 5:

j=3,i=2

b(2,3)=(b (3, 2)-b(2, 2))/(x(4)-x(2))

Step 6:

j=4,i=1

b(1,4)=(b (2, 3)-b(1, 3))/(x(4)-x(1))