ENGS 106: Numerical Linear Algebra



COSC 71 or ENGS 91. Students are to be familiar with approximation theory, error analysis, direct and iterative techniques for solving linear systems, and discretization of continuous problems to the level normally encountered in an undergraduate course in numerical analysis.

Identical to COSC 271

The course examines, in the context of modern computational practice, algorithms for solving linear systems Ax = b and Ax = lambdax. Matrix decomposition algorithms, matrix inversion, and eigenvector expansions are studied. Algorithms for special matrix classes are featured, including symmetric positive definite matrices, banded matrices, and sparse matrices. Error analysis and complexity analysis of the algorithms are covered. The algorithms are implemented for selected examples chosen from elimination methods (linear systems), least squares (filters), linear programming, incidence matrices (networks and graphs), diagonalization (convolution), sparse matrices (partial differential equations).