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Numerical methods of Linear Algebra for Sparse Matrices
В начало
Курсы
Осенний семестр
Магистратура
Num Methods 2025
Exam
Exam program
Exam program
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◄ Exam procedure
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Course overview 2025
Course textbook
Working with Matlab in SFedU and getting started
Exam procedure
Exam Tickets
Individual project description
Choose your variant before December 16
Useful materials
Your individual projects (project submission before January 13)
Lecture notes for Module 1
Practical assignment 1. Getting started with Matlab
Practical assignment 2. Matrix fundamentals: types and structures
Practical assignment 3. Vector and matrix norms. Existence of solution, solving linear system in Matlab
Practical assignment 4. Gram-Schmidt and QR-factorization
Practical assignment 5. Eigenvalues and their multiplicities, matrix factorizations, Hermitian and positive definite matrices
Practical assignment 6. Schur, LU- and Cholessky factorizations of Hermitian positive definite matrices. Solving linear systems using LU- and Cholessky factorizations.
Practical assignment 7. Condition number, computational costs, well- and ill-conditioned problems
Practical assignment 8. Permutations, reordering and fill-ins
Practical assignment 9. Sparse storage and sparse formats
Lecture notes for Module 2
Practical assignment 10. Comparison of direct and iterative methods for different sparse systems
Practical assignment 11. Classic iterative methods
Practical assignment 12. Arnoldi process and FOM
Practical assignment 13. Givens rotations and GMRES
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