This course is designed to provide students with a thorough understanding of the mathematical underpinnings of computational methods for linear systems, as well as the implementation and testing of various algorithms in software.

Lecture 1 | Course Overview and Background | lecture1 hw1

Lecture 2 | Computing e^At | lecture2 hw2

Lecture 3 | Integrals Involving e^At | lecture3 hw3

Lecture 4 | Decomposition Methods for Ax=b | lecture4 hw4

Lecture 5 | Decomposition Methods for Positive Definite (PD) Matrices | lecture5 hw5

Lecture 6 | Least Squares Problem, Householder and Serial Gram-Schmidt Orthogonalization
Methods |  lecture6 hw6

Lecture 7 |  Givens Orthogonalization Methods, Weighted Least Squares, and Computation
of Pseudo Inverse |  lecture7 hw7

Lecture 8 | Recursive Square-root & QR Updating for Least Squares and Kalman Filtering | lecture8 hw8

Lecture 9 | Linear Programming: Revised Simplex, and Interior Point Methods | lecture9 hw9

Lecture 10 | Unsymmetric Eigenvalue Problem | lecture10 hw10

Lecture 11 | Symmetric Eigenvalue Problem | lecture11 hw11

Lecture 12 | Singular Value Decomposition (SVD) | lecture12 hw12

Lecture 13 | Solution of Lyapunov Equation for Continuous and Discrete Systems |  lecture13  hw13

Lecture 14 | Riccati Equation – Solution for Optimal Control Problem | lecture14 hw14

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