Explore factorization-based sparse solvers and preconditioners in this comprehensive lecture by Xiaoye Sherry Li from Lawrence Berkeley National Laboratory. Delve into topics such as minimum degree ordering, greedy algorithms, separator techniques, multilevel intersectional ordering, and numerical pivoting. Learn about the differences between sparse and dense Gaussian elimination, and gain insights into static pivoting methods. Discover practical applications and theoretical foundations of these advanced numerical techniques, supported by relevant references for further study.