Math 5465

Numerical Analysis


Course Description

From Catalog:

A survey of the construction, analysis, and implementation of numerical algorithms in linear algebra, nonlinear equations and optimization, approximation by polynomials, quadrature, and ordinary differential equations. High-level programming language required.

The first semester of this course emphasizes numerical linear algebra including forward and backward error analysis (stability and conditioning), numerous matrix factorizations including the singular value deccomposition (SVD), QR, LU, Cholesky, etc. In addition, iterative algorithms for linear systems and eigenvalue problems are covered. A list of topics includes:

  • Working in Finite Precision Arithmetic
  • Error Analysis and Numerical Stability
  • Matrix Decompositions (Analysis of Algorithms)
  • Iterative Algorithms
  • Introduction to Nonlinear Equations

In the second semester (5466), we will discuss:

  • Approximation Theory
  • Nonlinear Equations and Optimization
  • Numerical Methods for ODEs
  • Survey of Topics for Further Study

Course Instructor: Jeff Borggaard

Regular office hours will be held in McBryde 528, times will be arranged at the first class meeting. Additional meeting times can be arranged by e-mail.

Course Resources

Selected reading material will be placed on reserve in the library.

This course will be managed using the Virginia Tech Scholar site.

Course Contract

Math 5465 - Numerical Analysis - Fall 2012

Professor

Jeff Borggaard, regular office hours will be held in McBryde 528. Students are invited to e-mail me at (jborggaard@vt.edu) to arrange an appointment.

Text

Numerical Linear Algebra, Trefethen and Bau, SIAM (link to SIAM page) as well as additional material.

Evaluation and Grading

Regular homework assignments constitute 50% of the grade. An in-class exam and take-home final exam will be worth 25% each.

Honor Code

You are encouraged to discuss regular homework assignments with other members of the class, however any submitted write-up and code to be graded should be your work alone. All exams (in-class and takehome) must be worked on independently.

Failure to follow these restrictions, and giving or receiving unauthorized aid or assistance on homework, in-class exams on the take-home final are Virginia Tech Honor System violations and cases will be filed.