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Numerical methods of Linear Algebra for Sparse Matrices
В начало
Курсы
Осенний семестр
Магистратура
Num Methods 2025
Module 2. Krylov subspace methods for sparse linea...
Lecture notes for Module 2
Lecture notes for Module 2
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Lecture 7. Summary. Overview of direct and iterative methods.pdf
Lecture 7.pdf
Lecture 8. Descretization of PDEs.pdf
Lecture 8. Summary. Descretization of PDEs.pdf
Lecture 9. Classic iterative methods.pdf
Lecture 9. Summary. Classic iterative methods.pdf
Lecture 10. Projection methods. 1D projection methods.pdf
Lecture 10. Summary. Projection methods. 1D projection methods.pdf
Lecture 11-12. Summary. Krylov Subspace methods. FOM and GMRES.pdf
Lecture 11. Krylov subspace projection methods. FOM.pdf
Lecture 12. Krylov subspace projection methods. GMRES.pdf
Lecture 13. Lanczos orthogonalization and biorthogonalization. Preconditioning techniques.pdf
◄ Practical assignment 9. Sparse storage and sparse formats
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Course overview 2025
Course textbook
Working with Matlab in SFedU and getting started
Individual project description
Choose your variant before December 16
Useful materials
Your individual projects (project submission and defense on December 30)
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
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
Practical assignment 10. Comparison of direct and iterative methods for different sparse systems ►