Computer Science and Numerical Methods Flashcards

Simpson's 1/3 rule for numerical integration requires the number of subintervals to be:

Answer: An even number

Simpson's 1/3 rule fits parabolas over pairs of subintervals, requiring an even total number of subintervals.

In a computer's memory hierarchy, which level provides the fastest access time?

Answer: CPU cache (L1/L2/L3)

CPU cache is located directly on or near the processor chip and has the fastest access time of all storage levels.

The classical 4th-order Runge-Kutta method (RK4) evaluates how many slopes per integration step?

Answer: 4

RK4 computes four weighted slopes k₁, k₂, k₃, k₄ and combines them to achieve fourth-order accuracy.

Which sorting algorithm has the best average-case time complexity?

Answer: Quicksort O(n log n)

Quicksort's divide-and-conquer strategy yields O(n log n) average complexity, superior to O(n²) algorithms.

Finite difference approximations for derivatives are derived from:

Answer: Taylor series expansion

Truncating the Taylor series expansion yields forward, backward, and central finite difference formulas.

LU decomposition is most advantageous when:

Answer: Solving the same linear system with multiple different right-hand sides

LU decomposition factors a matrix once, then each new right-hand side requires only inexpensive forward and backward substitution.