Math 5466

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 (5465) 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

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 Contract

Math 5466 - Numerical Analysis - Spring 2018


Jeff Borggaard, regular office hours will be held in McBryde 528 (Mondays 1-3pm). Students are invited to e-mail me at ( to arrange an appointment.

Course Resources


Approximation Theory and Methods, M.J.D. Powell, Cambridge University Press. Additional material will be provided or placed on reserve or posted on Canvas.

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

Evaluation and Grading

Regular homework assignments constitute 40% of the grade. Two midterm exams and a final project will be worth 20% 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 or 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 final project are Virginia Tech Honor System violations. If you have questions about what constitutes academic misconduct, please speak with me. I am required to file cases that I uncover and the normal sanction I will recommend is an F* as your final course grade. The * will indicates that a student has failed to uphold the values of academic integrity at Virginia Tech.