Course Objectives: To provide an introduction to the fundamental ideas of matrix computations. It emphasizes the design, analysis, and computer implementation of accurate and efficient algorithms and the sensitivity analysis of basic matrix problems.

Detailed Description:

• Norms and floating-point arithmetic.
• Cholesky factorization and symmetric positive definite linear systems of equations.
• LU factorization and general linear systems of equations.
• Sensitivity of problems and numerical stability of algorithms.
• Blocking algorithms for higher performance.
• QR factorization and linear least squares problems.
• Singular value decomposition.
• Eigenvalue problems - theory and computations
• Iterative methods for large sparse linear systems (including classic iterative methods and Krylov subspace methods with focus on the conjugate gradient method)
• Tensor decomposition (if we have time available).

Prerequisites: Facility with a high level programming language such as MATLAB, Python, and a good introductory matrix theory course. Previous experience of numerical computations is also important, such as COMP 350 or MATH 317. Some assignments will be done by MATLAB or other programming languages you prefer.