Introduction to fundamental linear algebra problems and their importance, computational difficulties using theoretical linear algebra techniques, review of core linear algebra concepts; introduction to matrix calculus; floating point representation; conditioning of problems and stability of algorithms; singular value decomposition and regularization theory.

Same as Reference

1. Datta, B. N., Numerical Linear Algebra and Applications, 2nd Ed., Siam (2010).

2. Demmel, J. W., Applied Numerical Linear Algebra, Siam (1997).

3. Lu, S. and Pereversev, S., Regularization Theory for Ill-posed Problems: Selected Topics

4. Walter de Gruyter GmbH, Berlin/Boston, Inverse and Ill-Posed Problems Series 58.

Course Outcomes  (COs):

CO1: Learn the basic matrix factorization methods for solving systems of linear equations and linear least squares problems.

CO2: Understanding basic computer arithmetic and the concepts of conditioning and stability of a numerical method.

CO3: Study the basic numerical methods for computing eigenvalues.

CO4: Learn the basic iterative methods for solving systems of linear equations.