Interpolation and curve fitting – MCQs – EE

1. What is the main purpose of interpolation?
(A) To find values within a given data range
(B) To estimate values outside the data range
(C) To differentiate a function
(D) To integrate a function

2. Which type of interpolation uses a straight line between two points?
(A) Linear interpolation
(B) Quadratic interpolation
(C) Cubic interpolation
(D) Spline interpolation

3. Quadratic interpolation uses:
(A) Two points
(B) Three points
(C) Four points
(D) Five points

4. Cubic interpolation is preferred when:
(A) Data is linear
(B) Smoothness is required
(C) Only two points are available
(D) Speed is more important than accuracy

5. Lagrange interpolation formula is used for:
(A) Linear approximation only
(B) Polynomial interpolation of any degree
(C) Spline fitting only
(D) Exponential data

6. Which method constructs the interpolating polynomial incrementally?
(A) Lagrange method
(B) Newton’s divided difference method
(C) Linear interpolation
(D) Cubic spline

7. Which type of interpolation ensures continuous first and second derivatives?
(A) Linear
(B) Quadratic
(C) Cubic spline
(D) Newton’s method

8. Runge’s phenomenon is associated with:
(A) Low-degree polynomials
(B) High-degree polynomial interpolation
(C) Linear interpolation
(D) Spline interpolation

9. Which method is more stable for high-degree interpolation?
(A) Lagrange polynomial
(B) Newton’s divided differences
(C) Cubic spline
(D) Linear interpolation

10. Curve fitting is mainly used to:
(A) Approximate a smooth function through data
(B) Find derivatives
(C) Find integrals
(D) Solve linear equations

11. Least squares method is commonly used for:
(A) Interpolation
(B) Curve fitting
(C) Numerical integration
(D) Numerical differentiation

12. In linear curve fitting, the relationship between variables is assumed to be:
(A) Linear
(B) Quadratic
(C) Exponential
(D) Logarithmic

13. Exponential curve fitting is used when:
(A) Data follows a straight line
(B) Data grows or decays exponentially
(C) Data is random
(D) Only two points are available

14. Polynomial curve fitting can be unstable if:
(A) Degree is too high
(B) Degree is too low
(C) Data points are few
(D) Both B and C

15. The sum of squared errors is minimized in:
(A) Interpolation
(B) Least squares curve fitting
(C) Linear approximation
(D) Cubic spline interpolation

16. Linear interpolation can cause errors if:
(A) Data is highly nonlinear
(B) Data is evenly spaced
(C) Only two points are used
(D) Step size is small

17. Newton’s forward difference is suitable for:
(A) Equally spaced data
(B) Unequally spaced data
(C) Random data
(D) None of the above

18. Newton’s backward difference is mainly used for:
(A) Starting points
(B) End points of data
(C) Random points
(D) Midpoints

19. Which method reduces oscillations in polynomial interpolation?
(A) Lagrange polynomial
(B) High-degree polynomial
(C) Cubic spline
(D) Linear interpolation

20. Curve fitting is necessary when:
(A) Exact function is unknown
(B) Data contains noise
(C) Prediction is required
(D) All of the above

21. Interpolation passes:
(A) Through all data points
(B) Near the data points
(C) Only through first and last points
(D) None of the above

22. In least squares fitting, the curve:
(A) Passes exactly through all points
(B) Minimizes the distance to points
(C) Ignores some points
(D) Passes only through first and last points

23. Which method is computationally simple and fast for small datasets?
(A) Linear interpolation
(B) Cubic spline
(C) Lagrange polynomial of high degree
(D) Newton’s method

24. Which method is preferred for large datasets requiring smooth curves?
(A) Linear interpolation
(B) Cubic spline
(C) High-degree polynomial interpolation
(D) Exponential fitting

25. In curve fitting, overfitting occurs when:
(A) Degree of polynomial is too high
(B) Degree of polynomial is too low
(C) Step size is small
(D) Data is evenly spaced

26. Linear regression is a type of:
(A) Interpolation
(B) Curve fitting
(C) Differentiation
(D) Integration

27. Newton’s divided difference method can handle:
(A) Equally spaced data only
(B) Unequally spaced data
(C) Random data only
(D) None of the above

28. Lagrange interpolation is easy to implement but:
(A) Computationally expensive for many points
(B) Less accurate for small data
(C) Only works for linear data
(D) Not used in EE

29. Cubic spline interpolation ensures:
(A) Continuous first derivative
(B) Continuous second derivative
(C) Both first and second derivatives continuous
(D) No derivative continuity

30. The main difference between interpolation and curve fitting is:
(A) Interpolation passes through all points, curve fitting approximates
(B) Curve fitting passes through all points, interpolation approximates
(C) Both are the same
(D) None of the above