third-order Newton’s interpolating polynomial

Answer 1

[William Rose]

@ِAbo Alqahtani,

Here is the start of a solution. You will learn a lot more about Matlab by finishing it yourself.

Good luck!

% Create vectors with the known data
%I changed the order of x3,y3 and x4,y4 so the points are increasing
x=[1,4,5,6];                        %known x values
y=[0,1.386294,1.609438, 1.791759];  %known y values
b1=y(1);
b2=(y(2)-y(1))/(x(2)-x(1));
b3=0;                       %edit this 
b4=0;                       %edit this 
b5=0;                       %edit this
xq=2;                       %query point
yq=b1+b2*(xq-x(1));         %edit this
fprintf('y(interp)=%.4f at x=%.4f.\n',yq,xq);

y(interp)=0.4621 at x=2.0000.

plot((1:.1:6),log(1:.1:6),'-b',x,y,'bx',xq,yq,'ro')
xlabel('x'), ylabel('y')
legend('y=ln(x)','known','interpolated','Location','SE')