Statistics and Numerical Methods: Unit IV: Interpolation, numerical differentiation and numerical integration

Exercise 4.2 [Newton's Divided Differences interpolation]

Solved Example Problems

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Statistics and Numerical Methods : Unit - IV : Interpolation, numerical differentiation and numerical integration : Exercise 4.2 [Newton's Divided Differences interpolation]

EXERCISE 4.2 [Newton's Divided Differences interpolation]

Using Newton's divided differences formula, solve the following problems

1. Find f (x).

[Ans. f (x) = x (x-1) (x-4) (x2 + 2x-5)]

 

2. Find the polynomial equation of degree four passing through the points.

(8, 1515), (7, 778), (5, 138), (4, 43) and (2, 3)

[Ans. y = x4 - 10x3 + 36x2 - 36x - 5]

 

3. If y (0) = -18, y (1) = 0, y (5) = - 248, y (6) = 0 and y (9) 13104, find y = f (x)

 [Ans. f (x) = (x – 1) (x – 3) x – 6) (x2 -+ x + 1 )]

 

4. Find ƒ (5).


 

5. Find the pressure of steam at 142° C using Newton's general formula.


 [Ans. 3.8986688]

 

6. Obtain the value of log10 656 given log10 654 given log10 654  = 2.8156,

log10 658 = 2.8182, log10 659 = 2.8189 and log10 666 = 2.8202. [A.U A/M 2017 R-13]

[Ans. 2.8169]

 

Statistics and Numerical Methods: Unit IV: Interpolation, numerical differentiation and numerical integration : Tag: : Solved Example Problems - Exercise 4.2 [Newton's Divided Differences interpolation]

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