Question 3 (a) Consides the data 00 025 05 05 (2) (i) Cousta uct the divided difference's table for the data (u...
Question 3 (a) Consider the data. 00 0 25 0.5 05 () Construct the divaded difference's table for the data (u) Construct the Newton form of the polynomial of lowest degree that interpolates /() at these points (3) (ii) Suppose that these data were generated by the function cos 2 ()=1+ 2 Use the next term rule to approximate the error Ip(z)- f() over the interval 0,0 5 Your answer should be a pumber 3 (b) Let F ((z) co+...
Let (xi , f(xi)), i = 0, . . . , 3, be data points, where xi = i + 2, for i = 0, . . . , 3. Given the divided differences f[x0] = 1, f[x0, x1] = 2, f[x0, x1, x2] = −7, f[x0, x1, x2, x3] = 9, add the data point (0, 3), find a Newton form for the Lagrange polynomial interpolating all 5 data points. 3. (25 pts) Let (r,, f()), 0,3, be data...
Co OCT/SOV013 Question 3 () Conesdes the data 0 25 00 Consa wct the drvaled daference s Lable for the data (2) () Consrwet the Newton forsn of the polynomsnl p(a) of lowe-t degree that tes polates /) nt these potse () (n) Suppose that these data wese generated by thhe fumton cos 21 J)-1 2 Use the nest term rule to appOInate the eror Ipl)-f)over the intessal 0,05 Your anves should be a numbes (3) (b) Let f)Co +ealco...