# Courses

## MA 522 - Matrix Theory and Numerical Linear Algebra I.Review of basic linear algebra from a constructive and geometric point of view. Factorizations of Gauss, Cholesky and Gram-Schmidt; determinants; linear least squares problems; rounding error analysis; stable methods for updating matrix factorizations and for linear programming; introduction to Hermitian eigenvalue problems and the singular value decomposition via the QR algorithm and the Lanczos process; method of conjugate gradients. (Same as CS 522.)Prerequisite: MA 322.Possible Instructors: Ovall, Ye.Status of Course: Course functioning each fall. |

## MA 537 - Numerical Analysis.Finite-precision (floating-point) arithmetic; solution of non-linear equations; approximation of functions; numerical differentiation and integration; numerical solution of ordinary differential equations. (Same as MA 537 and EGR 537.)Prerequisite: MA 322.Possible Instructors: Demlow, Ovall, Ye.Status of Course: Course functioning. |

## MA 622 - Matrix Theory and Numerical Linear Algebra II.Numerical solution of matrix eigenvalue problems and applications of eigenvalues; normal forms of Jordan and Schur; vector and matrix norms; perturbation theory and bounds for eigenvalues; stable matrices and Lyapunov theorems; nonnegative matrices; iterative methods for solving large sparse linear systems. |

## MA 625 - Numerical Methods for Differential EquationsNumerical methods for parabolic, hyperbolic, and elliptic problems in one or more spatial dimensions. Finite differences and elements. Shooting methods for parabolic equations. Multigrid and domain decomposition methods for elliptic equations.Prerequisite: MA 537 or consent of instructor.Possible Instructor(s): Demlow, OvallStatus of Course: Course functioning each spring. |