The subject is Intro to Numerical Methods - Comp Sci

-using first two points create a line find the error in the rest of points.

-using first three points create a quadratic find the error in the rest of points.

-using first four points create a cubic find the error in the rest of points.

just compute the error in the last point (4.5, 2) in each of the three polynomials of degree 1,2,3.

1) Use Matlab to get Newtons polynomial of degree 5. Do not simplify it to the polynomial in standard form.

2) By hand use Newtons and Lagranges methods to compute the polynomial of degree 2 using the first three points.

18.5 Given these data 1.6 2 2.5 3.2 4 4.5 x)2 814158 (a) Calculate f(2.8) using Newton's interpolating polynomials of order 1 through 3. Choose the sequence of the points for your estimates to attain the best possible accuracy. (b) Utilize Eq. (18.18) to estimate the error for each prediction