Question

Question 4 (16 Points) Use Neville's method to approximate V11 with the following function and values. Use this polynomial to approximate f(11). Using 4-digit rounding arithmatic. (a). f(x) = (x and the values Xo = 6, xı = 8, x2 = 10, x3 = 12 and X4 = 13. (b). Compare the accuracy of the approximation in parts (a).

Answer 1

f(x) = 5x at x=1 Mo = 6, 2,38, X2=10,83 =12, 44=13 Po wayo Po, 1 (1) bu (a)=Y, Po, 2(X) bo, 3(a) Þl,2601 62220) zYz bigla) ba,ula) $2,312) b1,410 $3,360) = y3 $2,y (9) biyen 64,41%) = 44 (1) - (x-2) bitteja where, (A) bij in a Cx-vj) bis- di-aj tosiajan Pl; ;'(X) yi, osien CS Scanned with CamScanner

boroC11) = yo = f(ad = f(6) 2.44949 bil (11) = f(x) = $18)= 2.828.43 Þ2,2 (11) = f(x) = f(0) = 3.16228 f(12) = 3.46410 bu,ucll) = flaus = f(13) = 3.60555. $3,3 (1)- finz) bos, Cll) = (2-2) borolll) – (4-70) bis, (a) Hord, 5 (11-8) (2.44949) - (11-6] [2182843) 6-8 7.34847- 14.14215 - 3.39684 - 2 $1,2(11) = (11-22) b1;11) - (11-01) $2,2!!!) X1-12 (11-10) [2.82843) - (11-8) [3:16228) 8-10 2.82843 - 9.48684 = 3.329205 -2 CS Scanned with CamScanner

$2,3() = (x2-x) $2,2(11) + CX-Xz) 53,3C1U X3-02 (12-10) [ 3.16228) + (11-10)[3.46410] 12-10 3,31319 , , (4) - ( 24-3) Ba, 301) + (1-1,254,41) a4-23 = (13-10 (3.46410] + [1l-12) (3.60555) 13-12 = 3.32265 Þ0,2 (11) = (2-x) bo,,(11) + (0-20) $1,2 12-10 = (10-11) [ 3.396841+ [11-6] [ 3.329205) 10-6 = 3.312296 $1,3(11) = [ 13-a) þ1,2(11)+ ( 11-2p) $2,3 (1 az-a (12-11) [ 3.329205) + (11-8) [ 3.31319) – 3.31719 12-8 CS Scanned with CamScanner

52,4(11) = [My-XJb2, 3(11) + (X-92] 53,4(117 14-02 -(13-11) (3.31319) +(11-101 ( 3.32265] 13-10 = 3: 31634 Þ0,3(01) = ( 13-23 bo, 2[11] + (0-20) b), 3(11). 13-20 = 112-11) [ 3.312296).+ (11-6] [ 3.31719) 12-6 = 3.316374 blylll) = (04-8) b1, 3(11) + (4-203 62,4(1) du-nl (13-11) [ 3. 31719] + [11-8)(3.31634) 13-8 - 3.31668 CS Scanned with CamScanner

Þory (11) = (xy-) Þo, 3(11) at (0-20) 1,4(11) 24-70 (13-11) ( 3.3163745+ [11-6) (3.31668) 13-6 = 3.316 592 fia)= Ja at 11 is 3.316592 by Neville's Algorithm. b) Actual value of Sil upto 4-digit rounding accmaly I r 3.31662 is 3.31659 it i By Neville's Erra is very small be Neligible. cs Scanned with CamScanner