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CSCI 8314 - F26 Lecture notes

  • Lecture 9 : Posted on: Mon 12 Oct 2026 08:53:24 AM CDT Topics: Back to graphs; paths in graphs; Perron Frobenius theorem; Powers of matrices; Notions of centrality; Page Rank;

  • Lecture 8 : Posted on: Mon 12 Oct 2026 08:57:11 AM CDT Topics: Reordering and permutations; Band reduction techniques; Reversed Cuthill Mc Kee; Multicoloring methods Minimal degree ordering and variants; Nested dissection; complexity for model problems.

  • Lecture 7 : Posted on: Mon Oct 5 06:31:50 PM CDT 2026 Topics: Introduction to Sparse linear systems; Versions of LU factorizations (dense case); Sparse Column Cholesky; Graph model for Sparse Gaussian Elimination; Rose and Tarjan's Fill path theorem.

  • Lecture 6 : Posted on: Sat Sep 26 05:54:32 PM CDT 2026 Topics: Graph models; Graphs and sparse matrices; Bipartitie representations; Hypergraphs; Application: paths in graphs; Markov chains (brief); Computational graphs; back-propagation.

  • Lecture 5 : Posted on: Sat Sep 26 05:50:07 PM CDT 2026 Topics: Triangular systems; Solving sparse triangular systems with sparse right-hand-sides. LU factorization from Sparse triangular solves

  • Lecture 4 : Posted on: Sun Sep 20 07:38:10 PM CDT 2026 Topics: Background on graph theory; general definitions; implementations; Paths and cycles; connected graphs; acyclic graphs; Graph traversals; Depth-First Search; Topological sorting;

  • Lecture 3 : Posted on: Wed 16 Sep 2026 09:47:38 AM CDT Topics: General data structures for sparse matrices; Sparse matrix formats; COO, CSR, CSC; etc. Matrix vector products

  • Lecture 2 : Posted on: Sat Sep 12 02:40:47 PM CDT 2026 Topics: Origins of sparse matrices; Typical problems; Discretization of Partial Differential Equations; Finite Differences and (In brief:) Finite Element methods

  • Lecture 1 : Posted on: Fri Sep 4 10:47:45 AM CDT 2026 Topics: Introduction; Types of problems seen in this course ; General introduction; Motivation; historical perspective; Pointers to resources; Sparse matrices - definition; Structured, unstructured sparsity; sparse matrices in matlab.