Math 430/630 - Matrix Analysis

Fall 2002 - Matthias K. Gobbert

Section 0101 - Schedule Numbers 3699/3730

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Basic Information


Matrix Analysis encompasses the theory of matrices as well as the practice of using numerical methods to implement the associated algorithms in a computer. The most classical example of a computational technique that is used both for hand calculations as well as in the computer is Gaussian elimination to find the solution to a linear system of equations; a version of this algorithm is known as reduction to row echelon form. Starting with knowledge from basic linear algebra, we will build up familiarity with advanced concepts and their application.

The course will start by introducing basic definitions like vector and matrix norms and the singular value decomposition. In addition to linear system of equations, we will study least-squares problems and eigenvalue computations, and various numerical methods to solve them. Those methods include both direct methods (that produce the solution in a fixed number of steps) and iterative methods (that get closer to the solution the more steps are taken). We will discuss advantages and drawbacks of both types of methods, based both on theoretical considerations and implementation details.

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This page version 2.5, December 2002.