Syllabus
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.
Text Books
Same as Reference
References
- Datta, B. N., Numerical Linear Algebra and Applications, 2nd Ed., Siam (2010).
- Demmel, J. W., Applied Numerical Linear Algebra, Siam (1997).
- Lu, S. and Pereversev, S., Regularization Theory for Ill-posed Problems: Selected Topics
- 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.