126 CHAPTER 3 - Interpolation and Polynomiel Approximation As might be expected from the evaluation of a and a1, the required constants are = flx0,X1,2....), for each k = 0,1,...,n. So P,(x) can be...

plz solve q1 part a equation 3.10 and algorathim is attached u can use any of them

Extracted text: 126 CHAPTER 3 - Interpolation and Polynomiel Approximation As might be expected from the evaluation of a and a1, the required constants are = flx0,X1,2....), for each k = 0,1,...,n. So P,(x) can be rewritten in a form called Newton's Divided- Difference: P(x) = fl%a]+£ S%o1.....(x- a) ... (x - 4-1). (3. 10) The value of f(xo, a...] isindependent of the arder of the numbers x0,X1..... , as shown in Exercise 21. The generation of the divided differences is out lined in Table 3.9. Two fouth and one fifth difference can akso be determined from these data. Table 3.9 Fist Secoal diided difkerenes Third divided diflecnces dividel difkerenes - flal- fll flal- flal flal flul- fal fl.al- fla.al Newton's Divided-Difference Formula ALGORITHIM 3.2 Toobtain the divided-difference coefficients of the interpolatory polynomial Pan the (n+ 1) distinct mumbers Xg, Xp. ..., for the function f: INPUT numbers Ag, X1. ...; values f(x). f (x),.... f(4) as Fan. F1,0 --. Fao OUTPUT the numbers Fao. F1.t ...Fan where P,(x) = Fop +EFJI«- x). (Fu is f[xg, X1. ....1.) Step 1 For i- 1, 2,...," For j=1,2...i Fu-- F-y- (Fu - fl..-) set Fy = Step 2 OUTPUT (Fan.Fu.....Fa): STOP.


Extracted text: 1. Use Eq. (3.10) or Algorithm 3.2 to construct interpolating polynomials of degree one, two, and three for the following data. Approximate the specified value using each of the polynomials. f(8.4) if ƒ (8.1) = 16.94410, f (8.3) = 17.56492, ƒ(8.6) = 18.50515, ƒ (8.7) = 18.82091 f (0.9) if f(0.6) а. b. -0.17694460, f (0.7) = 0.01375227, f(0.8) = 0.22363362, ƒ (1.0) 0.65809197