General form of Newtons interpolation polynomials is as foll

General form of Newton\'s interpolation polynomials is as follows f_n(x) = f(x_0) + (x - x_0) f[x_1, x_0\\ + (x - x_1] f[x_2, x_1, x_0] + ... + (x - x_0)(x - x_1)...(x - x_n-1) f[x_n, x_n-1, ...x_0] where f[x_i, x_j] - f[x_j, x_k]/x_i - x_j f[x_n, x_n-1 ..., x_1, x_0] = f[x_n, x_n-1, ...x_1] - f[x_n-1, x_n-2, ..., x_0] x_0 x_1 x_2 x_3 f(x_0) f(x_1) f(x_2) f(x_3) f[x_1, x_0] f[x_2, x_1] f[x_3, x_2] f[x_2, x_1, x_0] f[x_3, x_2, x_1] f[x_3, x_2, x_1, x_0] for n = 3 For the data in the table, develop a Matlab code to estimate f(0.7) with 1^st order, 2^nd order, 3 order, and 4^th order Newton\'s interpolation According to the pseudocode provided below!. Also estimate errors for each case. SUBROUTINF Newt Int (x, y, n, xi, yint, ea) LOCAL fdd_n.n DOFOR i = 0, n fdd_i.0 = Y_i END DO DOFOR j = 1, n DOFOR i - 0, n - j fdd_i, j = (fdd_i, j-1 - fdd_i, j-1)/(x_i+j - x_i) END DO END DO xterm = 1 yint_0 = fdd_0.0 DOFOR order = 1, n xterm = xterm * (x_i - x_order-1) yint2 = yint_order-1 + fdd_0.order * xterm ea_order-1 = yint2 - yint_order-1 yint_order = yint2 END order END Newt Int An algorithm for Newton\'s interpolating polynomial written in pseudocode.

Solution

function fp=forward_interpolation(x,y,p)
n=length(x);
for i=1:n
diff(i,1)=y(i);
end
for j=2:n
for i=1:n-j+1
diff(i,j)=diff(i+1,j-1)-diff(i,j-1);
end
end
answer=y(1);
h=x(2)-x(1);
s=(p-x(1))/h;
for i=1:n-1
term=1;
for j=1:i
term=term*(s+j-1)/j;
end
answer=answer+term*diff(1,i+1);
end
fp=answer;

Arguments sent to the function are:- lagrange(xdataset,ydataset,interpolating point)