Calculate f(4) using newton's interpolating polynomials of order 1 through 4. Choose your base points to attain good accuracy.

x = [1 2 3 5 7 8];
y = [3 6 19 99 291 444];

I know I need a polval function like

xx = 1:8;
yy = polyval(xx,n);

I just don't know where to go from there.

[Walter Roberson]

What is f(4) ?

[Quinten]

I think it's asking what is f(x) when x = 4 or it means 4th order polynomial

[Walter Roberson]

And what is f(x) ?

[Quinten]

i'm not sure, but i'm suppose to use newton's interpolating polynomial

[Jan]

@Quinten: We cannot guess, what f() is. Without knowing this detail, the question is not meaningful.

[Walter Roberson]

Is the assignment to do with being passed in a function handle, and you are to apply the interpolation for the passed function handle evaluated at parameter 4?

Answer 1

[Tamir Suliman]

Check this code though I m not sure

function newton_interpolation(x,y,n,xx)

% x and y are two Row Matrices 
% and xx is point of interpolation
% n is the order number which should be less than the matrix size

a(1) = y(1);
for k = 1 : n - 1
   d(k, 1) = (y(k+1) - y(k))/(x(k+1) - x(k));
end
for j = 2 : n - 1
   for k = 1 : n - j
      d(k, j) = (d(k+1, j - 1) - d(k, j - 1))/(x(k+j) - x(k));
   end
end
d
for j = 2 : n
   a(j) = d(1, j-1);
end
Df(1) = 1;
c(1) = a(1);
for j = 2 : n
   Df(j)=(xx - x(j-1)) .* Df(j-1);
   c(j) = a(j) .* Df(j);
end
fp=sum(c)
plot(x,y)

      title('Newton  Interpolation ')
      xlabel('x - value')
      ylabel('y - value')
      axis([min(x)-1 max(x)+1 0 max(y)+50])
      grid on