Assignment	Description
Program 1	Implement subroutines for computing the product and solving triangular systems for unit lower triangular and nonsingular upper triangular matrices. Develop these routines in preparation for an LU factorization implementation. Validate your routines through various tests, including properties of matrix products and system solutions.
Program 2	Implement and evaluate LU factorization of a full-rank matrix A using Gauss transforms and permutations. Explore different pivoting strategies: no pivoting, partial, and complete pivoting. Validate the factorization through empirical tests, and check the structure and performance across randomly generated problems.
Program 3	Develop and test two algorithms for solving the linear least squares problem: Householder transformations and an incremental algorithm. Implement tests to validate correctness across different problem sets and configurations. Also explore regularized linear least squares problems using a simple penalty term for noisy observation mitigation.
Project	Explore CUR decomposition, its applications in data science, and its advantages over other matrix factorizations like SVD and PCA. Focus on the interpretability and efficiency of CUR in large, sparse datasets. Analyze the mathematical and computational aspects, including the calculation of leverage scores and the impact on CUR's performance.