Lecture: Newton's Method and Fast Division

Background Material

• Lecture on FFT based integer and polynomial arithmetic
• Lecture on the Euclidean Algorithm

Reading

• Karl Hasselstrom, Fast Division of Large Integers, M.S. Thesis, Royal Institute of Technology, February 2003.
• Donald Knuth, The Art of Computer Programming, Vol. 2, 3rd Ed., Sec. 4.3.3D, 1998, pp. 311-313.

Topics

1. Newton's Method
2. Reciprocal Computation
3. Convergence of Newton's Method
4. Fast Division using Newton's Method

Slides and Worksheets

1. newton_div.mw - worksheet on Newton's method and fast division
2. Notes on convergence of Newton's method(Convergence.pdf)