Lecture 6: Fast Integer Multiplication

Background Material

Reading

Topics

  1. Review of classical Theta(n^2) algoritihm for multiplying integers.
  2. Divide and conquer recurrence: T(n) = a*T(n/b) + Theta(n).
  3. Recursive program to multiply integers [ a = 4, b = 2].
  4. Karatsuba's algorithm [a = 3, b = 2].
  5. Analysis of Karatsuba's algorithm.
  6. Multiplying integers in time Theta(n^(1+e)) for any e > 0.

Slides

  1. imult.ppt (imult.pdf) - slides covering Karatsuba's algorithm and generalizations.

Maple worksheets and other resources

Created: April 14, 2006 by jjohnson@cs.drexel.edu