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Bsc CSIT Semester 3 – Numerical Method – Unit 2: Interpolation and Regression (8 Hrs.)

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

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Write an algorithm and program to implement Lagrange interpolation method.

MediumNumerical10 marks2081(TU Final)

Consider the following data points estimate the f(0.6) using Newton’s interpolation formula.

x	0.1	0.2	0.3	0.4	0.5
f(x)	2.68	3.04	3.38	3.69	3.97

MediumNumerical5 marks2081(TU Final)

What is regression analysis? Fit a second order polynomial for the following data values.

x	2	4	6	8	10
y	1.4	2.0	2.4	2.6	2.8

MediumNumerical5 marks2081(TU Final)

Given the data points below

X	1.0	3.0	4.0
f(x)	1.5	4.5	9.0

Find cubic spline which belongs to $1<=x<=3$ and estimate $f(2)$ using cubic splines.

MediumNumerical5 marks2081(TU Final)

Define the terms interpolation and extrapolation. Write down the algorithm and program for Newton’s divided difference interpolation.

HardNumerical10 marks2080(TU Final)

Construct Newton’s backward difference table for given data points and approximate the value of f(x) at $x=45$ .

\begin{array}{|c|c|c|c|c|c|} \hline x & 10 & 20 & 30 & 40 & 50 \\ \hline f(x) & 0.985 & 0.934 & 0.866 & 0.766 & 0.643 \\ \hline \end{array}

MediumNumerical5 marks2080(TU Final)

Fit the quadratic curve through the following data points and estimate the value of f(x) at x=2.

\begin{array}{|c|c|c|c|c|c|} \hline x & 1 & 3 & 4 & 5 & 6 \\ \hline y & 2 & 7 & 8 & 7 & 5 \\ \hline \end{array}

MediumNumerical5 marks2080(TU Final)

How spline interpolation differs with the Langrage’s interpolation? Estimate the value of $f(0)$ and $f(4)$ using cubic spline interpolation from the following data.

\begin{array}{|c|c|c|c|c|} \hline \textbf{x} & -1 & 1 &2 & 3 \\ \hline \textbf{f(x)} &-10 &-2& 14& 86 \\ \hline \end{array}

HardNumerical10 marks2079(TU Final)

Fit the quadratic function for the data given below using least square method.

\begin{array}{|c|c|c|c|c|c|c|c} \hline \textbf{x} & 1.0 &1.5 &2.0 &2.5 &3.0 &3.5 &4.0\\ \hline \textbf{f(x)} &2.7 &4 &5.8 &8.3 &11.2 &15 &19\\ \hline \end{array}

MediumNumerical5 marks2079(TU Final)

How interpolation differs from regression? Write down algorithm and program for Lagrange interpolation.

HardNumerical10 marks2077(TU Final)

Define the terms true error and relative error? Use Horner’ method to evaluate polynomial $2x^3 - 3x^2 + 5x - 2$ at $x = 3$ and write down its algorithm.

MediumNumerical5 marks2077(TU Final)

Construct Newton’s forward difference table for the given data points and approximate the value of $f(x)$ at $x = 15.$

\begin{array}{|c|c|c|c|c|c|} \hline x & 10 & 20 & 30 & 40 & 50 \\ \hline f(x) & 0.173 & 0.342 & 0.500 & 0.643 & 0.766 \\ \hline \end{array}

MediumNumerical5 marks2077(TU Final)

Fit the curve $y = ae^{bx}$ through the following data points.

\begin{array}{|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 \\ \hline y & 1.65 & 2.70 & 4.50 & 7.35 \\ \hline \end{array}

MediumNumerical5 marks2077(TU Final)

What is Newton’s interpolation? Obtain the divided difference table from the following data set and estimate the f(x) at $x = 2$ and $x = 5.$

\begin{array}{|c|c|c|c|c|c|} \hline x & 3.2 & 2.7 & 1.0 & 4.8 & 5.6 \\ \hline f(x) & 22.0 & 17.8 & 14.2 & 38.3 & 51.7 \\ \hline \end{array}

MediumNumerical5 marks2078(TU Final)

What is linear regression? Fit the linear function to the following data

\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 & 2.2 & 2.4 \\ \hline f(x) & 2.0 & 2.6 & 3.9 & 6.0 & 9.3 & 15.0 & 20.6 & 30.4 \\ \hline \end{array}

MediumNumerical5 marks2078(TU Final)

What are the problems with polynomial interpolation for a large number of data set? How such problems are addressed? Explain with an example.

MediumNumerical5 marks2078(TU Final)

Showing 16 questions

Sample Questions

Write an algorithm and program to implement Lagrange interpolation method.

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

Consider the following data points estimate the f(0.6) using Newton’s interpolation formula. |x |0.1 |0.2 |0.3 |0.4 |0.5| |--|--|--|--|--|--| |f(x)| 2.68 |3.04| 3.38| 3.69| 3.97|

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

What is regression analysis? Fit a second order polynomial for the following data values. |x| 2 |4 |6| 8 |10| |--|--|--|--|--|--| |y |1.4 |2.0 |2.4 |2.6 |2.8|

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

Given the data points below |X |1.0 |3.0 |4.0| |-|-|-|-| |f(x)| 1.5| 4.5| 9.0| Find cubic spline which belongs to $1<=x<=3$ and estimate $f(2)$ using cubic splines.

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

Define the terms interpolation and extrapolation. Write down the algorithm and program for Newton’s divided difference interpolation.

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

And more questions available on this page.

Bsc CSIT Semester 3 – Numerical Method – Unit 2: Interpolation and Regression (8 Hrs.)

Sample Questions

Write an algorithm and program to implement Lagrange interpolation method.

Consider the following data points estimate the f(0.6) using Newton’s interpolation formula. |x |0.1 |0.2 |0.3 |0.4 |0.5| |--|--|--|--|--|--| |f(x)| 2.68 |3.04| 3.38| 3.69| 3.97|

What is regression analysis? Fit a second order polynomial for the following data values. |x| 2 |4 |6| 8 |10| |--|--|--|--|--|--| |y |1.4 |2.0 |2.4 |2.6 |2.8|

Given the data points below |X |1.0 |3.0 |4.0| |-|-|-|-| |f(x)| 1.5| 4.5| 9.0| Find cubic spline which belongs to \(1<=x<=3\) and estimate \(f(2)\) using cubic splines.

Define the terms interpolation and extrapolation. Write down the algorithm and program for Newton’s divided difference interpolation.