Introductory Numerical Analysis: Numerical Linear Algebra, Math 504 / CS 575 - Spring 2016

Time and Place:

13:00-13:50, MWF, Science & Math Learning Center 356.


Daniel Appelo, 277-3310, appelo kanelbulle

Required text book:

  1. G. Golub and C. Van Loan, Matrix Computations, 2013, Johns Hopkins University Press, distributed by SIAM.

Recommended text books:

  1. J. Demmel, Applied Numerical Linear Algebra, 1997, SIAM.
  2. L. Trefethen and D. Bau, Numerical Linear Algebra, 1997, SIAM.
  3. N. Higham, Accuracy and Stability of Numerical Algorithms, 2002, SIAM.
  4. C. Meyer, Matrix Analysis and Applied Linear Algebra, 2000, SIAM.
  5. A. Laub, Matrix Analysis for Scientists and Engineers, 2005, SIAM.

Office hours:

SMLC 310 Tuesday 13.00-15.00, Wednesday 15.30-17.00.


Prerequisites: MATH 464/514. I will also assume you have the basic skills of an applied mathematician or engineer in the field of computational science and engineering (The third pilar of science).

Description and goals:

From the course handbook: Direct and iterative methods of the solution of linear systems of equations and least squares problems. Error analysis and numerical stability. The eigenvalue problem. Descent methods for function minimization, time permitting.

The goals of this class are:

  • To acquire practical and theoretical knowledge of computational algorithms for numerical linear algebra.
  • To acquire a broad knowledge of the algorithms that are available for linear systems, linear least squares, eigenvalue problems.
  • To master proof techniques commonly used in numerical linear algebra.
  • To understand how to efficiently implement the algorithms and methods discussed in class on serial machines.
  • To understand what influences the efficiency of the implementations in serial and parallel (we will not actually implement the algorithms in parallel).
  • To understand what implications finite precision number systems have on the accuracy and stability of the algorithms we consider.

Homework / Computer Projects:

The homework will consist of weekly theoretical and computational assignments. The programs that are used for the computational assignments should be kept under version control using and must be shared with the instructor and TA. The computer programs should be written in Matlab, Fortran or C.

The homework reports should preferably be typed up. Grading will be made on the mathematical correctness, the correctness and style of the implementation and the overall style of the report.


There will be two midterm exams and a final exam. The exams will be oral. Each midterm will be 25 minutes per person and consist of board work solving one or two problems. You will have 25 minutes to prepare. The final will be in the same format but longer, approximately one hour. The exams will be pass or fail.


Your grade for this course is based on homework and computing projects, in-class work/attendance, and exams, in the following proportion: Homework/computing projects 75%, exams 25%.

To get a letter grade A you will have to pass all the exams on the first try.

After the weighted percentage grade has been calculated as detailed above, letter grades will be assigned according to the following scheme: A, 90 or above, B, 80 or above, C, 70 or above, D, 60 or above, F below 60. However, the instructor reserves the right to “curve” grades to offset unforeseen circumstances. The curving of grades will never decrease a student’s letter grade below that given by the above formula.

Dishonesty policy:

Each student is expected to maintain the highest standards of honesty and integrity in academic and professional matters. The University reserves the right to take disciplinary action, including dismissal, against any student who is found responsible for academic dishonesty. Any student who has been judged to have engaged in academic dishonesty in course work may receive a reduced or failing grade for the work in question and/or for the course. Academic dishonesty includes, but is not limited to, dishonesty on quizzes, tests or assignments; claiming credit for work not done or done by others; and hindering the academic work of other students.

American disabilities act:

In accordance with University Policy 2310 and the American Disabilities Act (ADA), academic accommodations may be made for any student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor’s attention, as the instructor is not legally permitted to inquire. Students who may require assistance in emergency evacuations should contact the instructor as to the most appropriate procedures to follow. Contact Accessibility Services at 505-661-4692 for additional information


I reserve the right to make reasonable and necessary changes to the policies outlined in this syllabus. Whenever possible, the class will be notified well in advance of such changes. An up-to-date copy of the syllabus can always be found on the course website. It is your responsibility to know and understand the policies discussed therein. If in doubt, ask questions.