16  Linear Systems

Many applications of linear systems (including optimization)

The usual intro to LU Role of pivoting Cholesky (+ other areas where pivoting is not needed) Block factorization, role of level 3 BLAS

General meaning of Schur complements SMW and auxiliary variable formulations Schur complements, covariance, precision, and conditioning

Condition estimation

Iterative refinement

Sparsity and dependencies Data sparse matrices Direct sparse solver ideas When do direct sparse solvers make sense? Fast and superfast solvers (fwd ref: signals)

Examples with various Markov chain computations, PageRank?