Lecture: Karatsuba's Algorithm for Integer Multiplication

Background Material

• Geometric series and recurrence relations
• Algorithm analysis, big Oh and Theta
• Matrices, matrix multiplication, identity, and inverse
• Maple programming

Reading

• GMP Library

Topics

• Arbitrary precision integers
• Classical algorithm for integer multiplication
• What is Maple doing?
• Karatsuba's algorithm for integer multiplication - an O(n^1.59) algorithm
• Computing time of Karatsuba's algorithm
• Deriving Karatsuba's algorithm using interpolation
• Generalizations of Karatsuba's algorithm - even faster integer multiplication

Maple worksheet and lecture slides

• karatsuba.mw - Maple worksheet implementing, analyzing, and investigating the classical and Karatsuba's algorithm for arbitary-precision integer multiplication.
• Lecture slides on Karatsuba's algorithm (imult.ppt,imult.pdf)

Resources

• GMP Library

Assignments