Question

Consider the following data points: (0.5, 2.2), (0.75, 1.78) and (1.4, 1.51), where each point is in the form (1;, fi), with fi = f(2) for some unknown function f. Find p2(2) with coefficients to 4 decimal places via Lagrange interpolation. Interpolate a value at r = 0.9. Given that į < f'" (c) < į on the interval (0.5, 1.4), estimate the error bounds.

Answer 1

Page No. Date Girin data (0.5, 2.2), (0.75, 178), and (1.4, 1.0) point, n=3 thus thus Langarrye guen by for n erbeting P(x) interpolatiss (x-X;) - f(x;) j=1 f (x2-x) inl. them n=3 Post Is REX) =fafy – x3)(x - x2) + f(xt X-X,)(x-x2 (X.-X (X-X) (x2-x1(x2-x) + f(x) ( x - X.) (x-xz) (Xyx) (X; - X2) (X-0.75) (X-1.4 (05-075) (0-5-1-4) X 2.2 + 1.78 li (X-0.5).(X-3-4 Х (0.75-0:52 (0.75=1.4) + (x-0.5) (X-0.75 (1.4-0.5) 11:4-0-75) ISI 1.9 %. + 0.7 x 178 (x2.2.15X + 1.05 ) x 2.2 (x? + 0-225 X?- 1.25x + 0.375) X1:51 + 0.585 (-64625) Van .

Page No. Date 9.7777 x2 21-0922x + 10.2666 +10:9538 x2 + 20.8123 X to 7.6676 + 2-5P X2- 3.2264 x + 0.9679 Ply) 1-4043x² 3:4363 x + 3.5669 2 → reg. intepolated P2 (x) Post I X=o.g this plag) = B(x) 11 111 P2 (89) 1:40638697 - 3:4363x0.97 9.5669 1-6117 11 this P (2) Zones 1-6117 R(2) E Sit. zn is enor tem. and a е Post I The bound of & erra ever by the 7 C [a,b] of Pn of Pn inpool pul if(+?cc n! cos, la ca n=2 F"(x2 3 P"(x) they 2X3! 3x3! the i Exx) reg. bound to ma se 2 5 2 ve 31 5 12