CPSC 302: Numerical Computation for Algebraic Problems
2017/2018 Winter Term 1 (September-December 2017)
Mon/Wed/Fri 13:00-14:00, DMP 301
Tentative Course Outline
- Numerical Algorithms and Errors
- Scientific computing
- Problem conditioning and algorithm stability
- Floating point systems
- The IEEE standard
- Roundoff error accumulation and cancellation error
- Nonlinear Equations in One Variable
- Bisection method
- Fixed point iteration
- Newton's method and variants
- Minimizing a function in one variable
- Review of Linear Algebra
- Basic concepts
- Vector and matrix norms
- Special classes of matrices
- Singular value decomposition (SVD)
- Direct Methods for Linear Systems
- Gaussian elimination and backward substitution
- LU decomposition
- Pivoting strategies
- Efficient implementation
- The Cholesky decomposition
- Banded matrices and sparse matrices
- Estimating errors and the condition number
- Linear Least Squares Problems
- Data fitting
- Least squares and the normal equations
- QR decomposition
- Householder transformations and Gram-Schmidt orthogonalization
- SVD and truncated SVD
- Iterative Methods for Linear Systems
- Poisson equation
- Stationary iteration and relaxation methods
- Convergence of stationary methods
- Gradient descent methods
- Conjugate gradient method
- Preconditioning
- Small to Moderate-Sized Eigenvalue Problems
- Power method
- Inverse power method
- PageRank
- QR iteration