Chapter Study

BCA Semester 4 – Numerical Methods – Unit 2: Interpolation and Approximation (8Hrs.)

Comprehensive questions and detailed answers for Unit 2: Interpolation and Approximation (8Hrs.). Perfect for exam preparation and concept clarity.

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1

Estimate the value of ln⁡(2.5) using Newton-Gregory forward difference formula given the following data:

MediumTHEORY5 marks2021(TU FOHSS Final)

2

Given the data points:

i	0	1	2
$X_i$	9	16	25
$f_i$	3	4	5

Estimate the function value of fat $x = 14$ using cubic splines.

MediumTHEORY10 marks2021(TU FOHSS Final)

3

What are the advantages of Lagrange's formula over Newton's formula? When Newton's forward interpolation formula is used?

MediumTHEORY5 marks2022(TU FOHSS Final)

4

Find the polynomial that interpolates $f(0) = 0, f(1) = 1, f(2) = 0, f(3) = 1, f(4) = 0$ using Newton divided differences. Use the Newton table to generate the necessary divided differences.

MediumTHEORY5 marks2022(TU FOHSS Final)

5

Estimate the value of $sin θ$ at $θ = 45°$ using Newton's backward difference formula from the following set of data.

$\theta$	10	20	30	40	50	60
$sin \theta$	0.1736	0.3420	0.5000	0.6428	0.7660	0.8660

MediumTHEORY5 marks2023(TU FOHSS Final)

6

a) Fit a straight line to the following set of data using Least Square Regression.
b) Apply the factorization method (any) to solve the equations:

\quad \quad 2x + 3y + 7z =4

\quad \quad2x + 3y + z = 5

\quad \quad 3x + 4y + z = 7

MediumTHEORY10 marks2023(TU FOHSS Final)

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Sample Questions

Estimate the value of ln⁡(2.5) using Newton-Gregory forward difference formula given the following data:

Marks: 5Chapter: Unit 2: Interpolation and Approximation (8Hrs.)

Given the data points: |i|0|1|2| |-|-|-|-| |\(Xi\)|9|16|25| |\(fi\)|3|4|5| Estimate the function value of fat \(x = 14\) using cubic splines.

Marks: 10Chapter: Unit 2: Interpolation and Approximation (8Hrs.)

What are the advantages of Lagrange's formula over Newton's formula? When Newton's forward interpolation formula is used?

Marks: 5Chapter: Unit 2: Interpolation and Approximation (8Hrs.)

Find the polynomial that interpolates \(f(0) = 0, f(1) = 1, f(2) = 0, f(3) = 1, f(4) = 0 \)using Newton divided differences. Use the Newton table to generate the necessary divided differences.

Marks: 5Chapter: Unit 2: Interpolation and Approximation (8Hrs.)

Estimate the value of \(sin θ \) at \(θ = 45°\) using Newton's backward difference formula from the following set of data. |\(\theta\)|10|20|30|40|50|60| |-|-|-|-|-|-|-| \(sin \theta\)|0.1736|0.3420|0

Marks: 5Chapter: Unit 2: Interpolation and Approximation (8Hrs.)

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