EIT Computer Science and Numerical Methods 2 — Questions and Answers
Question 1: Gaussian elimination is used to solve:
- Ordinary differential equations
- Systems of linear algebraic equations (Correct answer)
- Partial differential equations
- Eigenvalue problems only
Correct answer: Systems of linear algebraic equations
Gaussian elimination uses elementary row operations to reduce a linear system to upper triangular form for back-substitution.
Question 2: What is the hexadecimal equivalent of decimal 255?
- FA
- FF (Correct answer)
- F0
- EF
Correct answer: FF
255 = 15×16¹ + 15×16⁰ = FF in hexadecimal.
Question 3: Euler's method for solving ODEs advances the solution using:
- Exact analytical integration
- Laplace transforms
- A forward difference approximation of the derivative (Correct answer)
- Backward elimination
Correct answer: A forward difference approximation of the derivative
Euler's method uses yₙ₊₁ = yₙ + h·f(xₙ, yₙ), a first-order forward difference step.
Question 4: A high condition number for a matrix indicates that the corresponding linear system is:
- Well-conditioned and stable
- Numerically ill-conditioned and sensitive to perturbations (Correct answer)
- Symmetric and positive definite
- Guaranteed to have no solution
Correct answer: Numerically ill-conditioned and sensitive to perturbations
A high condition number means small changes in the input data cause large changes in the solution.
Question 5: Among bisection, false position, secant, and Newton-Raphson methods, which converges fastest near a simple root?
- Bisection method
- False position method
- Newton-Raphson method (Correct answer)
- Secant method
Correct answer: Newton-Raphson method
Newton-Raphson achieves quadratic (second-order) convergence, doubling correct digits each iteration.
Question 6: Big-O notation O(1) describes an algorithm whose run time:
- Grows linearly with input size
- Grows logarithmically with input size
- Is constant regardless of input size (Correct answer)
- Grows quadratically with input size
Correct answer: Is constant regardless of input size
O(1) (constant time) means the algorithm takes the same amount of time regardless of input size.
EIT Computer Science and Numerical Methods 2
Gaussian elimination is used to solve: