Statistics and Numerical Methods: Unit IV: Interpolation, numerical differentiation and numerical integration
Short Questions and Answers
Newton's Divided Differences interpolation
Statistics and Numerical Methods : Unit - IV : Interpolation, numerical differentiation and numerical integration : Short Questions and Answers
SHORT QUESTIONS AND ANSWERS
1.
Give the Newton's divided difference interpolation formula :
Solution
: [A.U Trichy A/M 2010] [A.U A/M 2019 R-13]
f(x)
= f(x0) + (x – x0) f (x0,x1) + (x −
x) (x – x1)f (x0,x1,x2) + ….
+ (x – x0) (x – x1)...
(x –xn-1) f (x0,x1,...,xn)
2.
What is the nature of nth divided differences of a polynomial of nth degree?
Solution:
The
nth divided differences of a polynomial of degree n are constants.
3.
Find the divided difference of f (x) = x3 + x + 2 for the arguments
1, 3, 6, 11. [A.U CBT N/D 2010], [A.U. A/M 2011] [A.U N/D 2020 (R-17) NM] [A.U
A/M 2021 (R-17) NM]
Solution
:
The
divided difference table is
4.
State any two properties of divided differences. [A.U. M/J 2014, R8], [A.U N/D
2016 R13]
Solution
:
(i)
The divided differences are symmetrical in all their arguments. i.e., the value
of any difference is independent of the order of the arguments.
(ii)
The divided differences of the sum or difference of two functions is equal to
the sum or difference of the corresponding separate divided differences.
5.
Find the second divided differences with arguments a, b, c if f (x) = 1 / x
Solution:
7.
If f(x) = 1/x find f(a, b) using divided difference table. [A.U
CBT N/D 2011] [A.U Trichy N/D 2011]
Solution:
Given:
f(x) = 1/ x
Statistics and Numerical Methods: Unit IV: Interpolation, numerical differentiation and numerical integration : Tag: : Newton's Divided Differences interpolation - Short Questions and Answers
Statistics and Numerical Methods: Unit IV: Interpolation, numerical differentiation and numerical integration
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Statistics and Numerical Methods
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