Cmput 418 - Honours Numerical Methods

Instructors

Lectures:

Labs:

Objectives

To obtain a working knowledge of how to apply numerical methods to real-world problems and a thorough understanding of the mathematics and properties of these methods.

Syllabus

Numerical Computing basics

Linear Equations Some real world applications and motivations, Gauss and Gauss-Jordan Elimination, LU factorization, Sensitivity and Conditioning, Overdetermined systems and Linear Least Squares, methods for QR factorisation, Linear Regression, Data Fitting and Interpolation, Eigenvalue Problems, methods for Eigen and SVD factorizations.

Nonlinear Equations and Optimization Basic 1D search methods with and without derivatives. Convergence rates and stopping criteria, Multidimensional root finding. Conditions for extrema, local and global min and max. Unconstrained optimization, Broyden and CG methods. Constrained optimization, Comparison of root finding and optimization, Trust region methods, Homotopy methods and Embeddings.

Numerical Integration and Differentiation Numerical Quadrature, Numerical Differentiation, Richardson Extrapolation.

Mathematical Modeling of Real world problems Throughout the course examples of real world problems will be mathematically modeled and computationally solved.

Schedule

Grading

exams:

Written assignments

Lab assignments

Project (Optional):

MCM:

A grade of "satisfactory" requires a working knowledge of how to apply numerical methods to solve real world mathematical problems. For higher grades additionally an understanding of the mathematical derivation of numerical methods and their properties will be required.

Literature

Michael T. Heath: Scientific Computing. An Introductory Survey, 2nd Ed McGraw Hill 2002
Heath provides a mathematically careful treatment of core topics.
(Optional) Cleve Moler Numerical Computing with MATLAB SIAM books 2004. y
A more hands on introduction to numerical computing in Matlab

Communication

Directions to lecture classrom

BS G 110 is in the BioSciences building, the brick building behind the new glass building CCIS. The BS building is roughly H-shaped and G110 is in the western end of the central part, floor 1. Those who are familiar with the old location of the faculty of science admin and Deans offices can go there, and BS G110 is nearby in the same hallway. http://www.campusmap.ualberta.ca/?b=bs The closest path from CS involves walking to the loading dock on the west side of BS, entering up the short stairs to a door next to the loading dock. Once inside the building go down 1 stair level, and locate the G hallway to the east. (The different hallways have different letters preceding the room number.)

CS department course policies

A message from the university administration:

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