Lecture 9: FFT Based Polynomial and Integer Multiplication

Background Material

• Induction to Algorithms, T. Cormen, C. Leiserson, R. Rivest, McGraw Hill, 1990.
• Elements of Algebra and Algebraic Computing, John D. Lipson, Benjamin Cummings Publishing Co., 1981.
• Algorithms for Discrete Fourier Transform and Convolution, R. Tolimieri and M. An and C. Lu, Springer-Verlag 1989.

Reading

• Chapter 9 (pp. 300-312) of Lipson (handout, see above for reference).

Topics

1. Go over Assignment 5. See sol5.mws for my solution and an elaboration.
2. Mod p Fourier transforms
3. FFT-based polynomial multiplication
4. FFT-based integer multiplication (3-primes algorithm)

Lecture Slides

1. fast.ppt - power point slides containing lecture notes on mod p FFTs and FFT-based polynomial and integer multiplication.

Maple worksheets and programs

• fft.mws - Worksheet containing an implementation of a recursive FFT.
• sol5.mws Solution to assignment 5.

Assignment

• Final Exam