2.1 Solution of triangular systems2.2 LU factorization and Gaussian elimination2.3 Pivoting strategies and iterative refinement2.4 Systems with special properties2.4.1 Positive definite systems2.4.2 Tridiagonal systems of equations2.4.3 The Sherman–Morrison formula2.5 Accuracy issues, error estimations2.5.1 Norms2.5.2 Singular value decomposition (SVD)2.5.3 Error analysis and conditioning2.5.4 Rounding error analysis of Gaussian elimination2.6 Iterative methods2.6.1 Convergence of iterative refinement2.6.2 Spectral radius and convergence of a matrix2.6.3 Special iterative methods2.6.4 Outlook: advancements in iterative methods2.7 Exercises