Общее
Yosef Saad. Iterative Methods for Sparse Linear Systems
Тематический план
- Общее
- Module 1. Lecture 1
Module 1. Lecture 1
Lecture 1. Background in Linear Algebra. Basic definitions. Types and structures of square matrices.
- Lectures 2-5
Lectures 2-5
Lecture 2 Vector and matrix norms. Range and kernel. Existence of Solution. Orthonormal vectors.
Lecture 3. Gram-Schmidt process. Eigenvalues and their multiplicities. Basic matrix factorizations and canonical forms: QR, diagonal form, Jordan form, Schur form.
Lecture 4. Basic matrix factorizations: SVD, LU, Cholessky. Properties of normal, Hermittian matrices and positive definite matrices.Lecture 5. Perturbation analysis and condition number. Errors and costs.