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Numerical Methods of Linear Algebra 2026
В начало
Курсы
Весенний семестр
Магистратура
Num Methods 2026
Lectures
Lecture 15. FOM and GMRES. Lanczos process. Precon...
Lecture 15. FOM and GMRES. Lanczos process. Preconditioning techniques
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◄ Lecture 14. Krylov subspace methods. GMRES
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!!! Working with Matlab in 2026
Course overview 2026
Course textbook
Getting started with Matlab
Lecture recordings
Lecture topics with dates
Lecture 1. Fundamentals of Linear Algebra. Introduction of elementary notation
Lecture 2. Types and structures of square matrices. Vector and matrix norms
Lecture 3. Existence of solution. Orthogonality, Gram-Schmidt, QR
Lecture 4. Matrix factorizations (QR, LU, Cholesky)
Lecture 5. Eigenvalues multiplicities. Canonical forms. Diagonal, jordan, schur, svd
Lecture 6. Positive definite, Normal and Hermitian matrices. Perturbation analysis
Lecture 7. Graph representations of sparse matrices. Permutations and reordering
Lecture 8. Storage schemes for sparse matrices. Discretization of PDE (overview)
Lecture 9. Discretization of PDEs. Finite difference method
Lecture 10. Overview of FEM. Direct and iterative methods. General formulation of iterative method
Lecture 11. Classical iterative methods
Lecture 12. Projection methods. 1D projection methods
Lecture 13. Krylov subspace methods. FOM
Lecture 14. Krylov subspace methods. GMRES
For Lecture 15. Derivation of CG
Exam procedure
Exam program
For Lecture 15. Derivation of CG ►