Numerical Analysis

V63.0252
Spring 2007, Mondays and Wednesdays, 2:00 - 3:15 pm, Silver 802

Instructor: Olof Widlund

  • Coordinates of Olof Widlund
    Office: WWH 712
    Telephone: 998-3110
    Office Hours: Mondays 3:30 - 4:30 pm and Thursdays 4:00 - 5:00 pm. You can also try to drop in or send email or call for an appointment.
    Email: widlund@cims.nyu.edu

  • Final exam will be held on Monday May 7, 2:00--3:50 pm in the regular class room, Silver 802.
  • You can bring one sheet of regular sized paper covered by your own notes on both sides to the exam.

  • Text book: An Introduction to Numerical Analysis by Endre Suli and David Meyers. Cambridge University Press. (Homework assignments will often be from this book.

  • Handouts, which form an important part of the reading. Please request them by e-mail if you do not have copies:
  • Chapters 2, 3, and 4 (pp. 5-24) on Floating Point Numbers from:
    Numerical Computing with IEEE Floating Point Arithmetic by Michael L. Overton, SIAM.
  • Lectures 20 and 21 (pp. 147-162) on Gaussian Elimination and Pivoting.
  • Lecture 10 (pp. 69-76) Householder Triangularization.
  • Existence and Uniqueness of the Interpolating Polynomial (pp. 38-43).
  • Numerical Integration: Some Basic Rules and Adaptive Quadrature (pp. 303-309 and 328-331).

  • Course content. All page and section references are to the textbook.
  • Floating point arithmetic (handout).
  • When is function evaluation well- or ill-posed? (p. 69.)
  • Solution of nonlinear equations: Chapter 1, in particular rates of convergence. The Illinois method as an example of a hybrid method.
  • Linear systems of algebraic equations: Chapter 2 and handouts. Norms of vectors and matrices. Condition numbers of matrices. Least squares. Householder triangularization and how it provides and alternative to setting up and solving the normal equations. Special matrices; Sections 3.1-3.3.
  • Polynomial interpolation; Chapter 6 and handout. Lagrange and Hermite interpolation. Newton's approach. Error of polynomial interpolation. Runge's phenomena and the use of the zeros of Chebyshev polynomials as interpolation points.
  • Splines; Sections 11.1-11.5.
  • Numerical integration; Sections 7.1-7.3 and 7.5 and handout. Adaptive Simpson.
  • Inner product space. Gram-Schmidt. Best approximation in the 2-norm. Orthogonal polynomials. Sections 9.1-9.4.
  • Gaussian quadrature and the connection with orthogonal polynomials. Radau and Lobatto quadrature; the basic idea. Sections 10.1-10.3 and 10.6.
  • Best approximation of continuous functions with respect to the maximum norm. Chapter 8.
  • Reducing real symmetric matrices to tridiagonal form by using Householder transformations. Computing the determinant of tridiagonal matrices using a three term recurrence. Sturm sequences and how to use them to compute eigenvalues of symmetric tridiagonal matrices. Sections 5.5 and 5.6.


  • Introductions to MATLAB, courtesy Julie Cameron and Jessica Lin
  • Cambridge University Engineering Department -"Getting Started" and Example PDFs.
  • The official Matlab page - detailed with a lot of information.
  • Or from the same outfit
  • Wikipedia thread for Matlab - easy read, simple programs that are easy to comprehend

  • Midterm
    The midterm exam will be on Monday, March 5. It will cover material from the first three chapters of the text as well as the handout on Floating Point systems. Please review the homework assignment in preparation for the exam. You can bring one sheet of regular sized paper covered by your own notes on both sides to the exam.
  • Homework
    There will be regular homework assignments. Scores will be available on Blackboard. It is important that you do the homework yourself, but when you get stuck,I encourage you to consult with other students or me, to get help when necessary. However, when you get help, it is important to acknowledge it in writing. Please staple everything together and order the problems in the same order as given. The best way of turning in homework is to give it to me personally, in class or in my office. If I am not in my office, you can slide it under my door. If you put your homework in my mailbox, it is at your own risk.


  • Homework Assignments:
  • Homework set 1 Assigned January 24, due at midnight Monday February 5.
  • Homework set 2 Assigned February 1, due at midnight Monday February 19.
  • Homework set 3 Assigned February 16, due at midnight Friday March 9.
  • Homework set 4 Assigned March 26, due at midnight Monday April 9.
  • Homework set 5 Assigned March 26, due at midnight Monday April 16.
  • Homework set 6 Assigned April 6, due at midnight Wednesday April 25.


  • Lectures
  • January 17, 22, and 24: A discussion of floating point systems and arithmetic. A handout given out from
    Numerical Computing with IEEE Floating Point Arithmetic by Michael L. Overton, SIAM.