University of Puerto Rico
Department of Computer Science

Mate. 4061 - Numerical Analysis I

General Information

Room: C-311
Time: Tuesday and Thursday 4:00 to 5:20
Text: Timothy Sauer, Numerical Analysis , Addison Wesley, 2005

Professor: Yiannis Koutis
Office: Computer Science Department, ask Rosa Santiago.
Extension: 5035
Email: ioannis.koutis @upr.edu
Office hours: Tuesday and Thursday 3:00 to 4:00 (and by appointment)

Homeworks

Homework 1 (due March 17)
Homework 2 (due April 7)         [also mesh2dL.m]
Homework 3 (due May 10)
Homework 4 (due June 2)

BONUS POLICY: Bonus questions from all homeworks don't have deadlines. If you feel you want to improve or secure your grade, you can get more credit by solving past bonus problems.

Announcements

~~~!!!! Exam 1 !!!!!~~~: April 7, during class. Material in Sections 0-2 of textbook.

NO CLASS ON THURSDAY 5/19

~~~!!!! Exam 2 !!!!!~~~: May 31, during class. Material in Sections 3,4,10 of textbook.

March 15 lecture iterative methods
May 10    lecture on Strassen's algorithm and FFT for polynomial multiplication

Course Description

Numerical analysis is the study of algorithms for computing numerical solutions to mathematical problems. The course provides an introduction to the ideas of numerical analysis via simple problems in analysis and algebra. We will study the efficiency of the algorithms as well as their implementation. .

Topics and reviews

• Representation of floating point numbers, their implementation on the computer, loss of significance.
• Basic methods for finding solutions of nonlinear scalar equations and convergence analysis: bisection method, fixed point iteration, Newton method and secant.
• Systems of linear equations: Gaussian elimination, LU factorization, error analysis, variants of Gaussian elimination and iterative methods.
• Exam I
• Interpolation and approximation of functions: polynomial interpolation, divided differences Newton, Lagrange interpolation representation of pieces.
• Least Squares for inconsistent systems of equations: Gram-Schmidt orthogonalization, Householder operators, Gauss-Newton method
• Trigonometric interpolation and the Fast Fourier Transform.
• Comprerssion, the Discrete Cosine Transorfm (DCT) and
• Exam II

Evaluation

1. Two (2) exams: 50%
2. Assignments and projects: 50%

Assignments must be submitted at the beginning of class the day they are assigned. 5 .0% is deducted per day for late work.