CS W4241 - Numerical Algorithms and Complexity
Spring 2013
Monday, Wednesday, 4:10 - 5:25 pm
Professor: Joseph F. Traub
Office Hours: TBA
TA: TBA
Grading:
- Midterm 30%
- Final 40%
- Homework 30%
- Extra credit homework 10%
- TOTAL 110%
The course consists of two parts, complexity and algorithms.
PART I - COMPLEXITY
Rather than a text IŽll give you handouts.
The following is an indication of the topics IŽll cover.
- Overview
- Integration Example
- Breaking the Curse
- Mathematical Finance
- Model of Computation
- Formal Models and Scientific Knowledge
- Complexity of Linear Programming
- Complexity of Verification
- Clock Synchronization in Distributed Networks
- Assigning Values to Mathematical Hypotheses
OPTIONAL MATERIAL
- General Formulation of Information-Based Complexity
- Integration Example Concluded
- Value of Information in Computation
A number of additional complexity topics will be covered in the lectures. There will be handouts for this material also. Topics include
- Playing 20 questions against a liar
- Continuous binary search
- Fast matrix multiplication
- Fast Fourier transform (FFT)
- Polynomial Evaluation
- Effect of precomputation
PART II - ALGORITHMS
The material on algorithms will be covered by handouts.
- Nonlinear Equations
- Univariate
- Multivariate
- Polynomial zeros
- Bernoulli algorithm
- Jenkins - Traub algorithm
- Randomization
- High dimensional integration
- Numerical solution of partial differential equations
- Elliptic equations
- Parabolic equations
- Hyperbolic equations
- Applications to science, engineering, finance.
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