AMSC/CMSC 666 Catalog Description

AMSC 666, Numerical Analysis I (3 credits):
Iterative methods for linear systems, piecewise interpolation, eigenvalue problems, numerical integration.

Details and Syllabi

Prerequisites

AMSC/CMSC 460 or 466 or equivalent background in numerics
MATH 410 or equivalent background in analysis

Syllabus

Interpolation and Approximation (Chapter 2)
- Polynomial Interpolation, Uniform Approximation, Rational Approximation, Trigonometric Interpolation, Splines.
Numerical Integration (Chapter 3)
- Newton-Coates Formulas, Peano Kernel Theorem, Euler-Maclaurin Formula, Romberg Integration, Gaussian Integration, Adaptive Quadrature.
Eigenvalue Problems (Chapter 6)
- Normal Forms, Rayleigh Quotient, Singular Value Decompositions, Power and Inverse Power Methods, QR Algorithm, Eigenvalue Perturbation Theory.
Iterative Methods for Linear Algebraic Systems (Chapter 8)
- Classical Methods, Conjugate Gradient Method, Preconditioning, GMRES.