MATH 4165: Numerical Linear Algebra

University of North Carolina, Charlotte

Matrix norms and condition numbers. Direct methods for linear systems and their accuracy and stability. Iterative methods for large sparse linear systems and their convergence. Least squares methods for non-square linear systems. Matrix Decompositions (LU and Cholesky Decompositions, Rank Decomposition, QR decomposition; Eigendecomposition and Diagonalization, Singular Value Decomposition). Efficient matrix multiplication methods. Matrix approximations. Matrix phylogeny. Examples of numerical linear algebra in machine learning.