no of classes |
TOPICS |
|
2 |
Fundamental Concepts • Matrix-Vector operations • Orthogonal vectors and matrices • Matrix and vector norms • Singular value decomposition (SVD) |
lect1 lect2 lect3 matlab1 matlab2 matlab3 |
6 |
QR Factorization • Projectors and QR factorization • Gram-Schmidt orthogonalization process • Householder triangularization • Least-squares problems |
qr pagerank least_square |
6 |
Conditioning and Stability • Condition numbers • Floating point Arithmetic • Stability • Conditioning of Householder triangularization • Conditioning of Back substitution • Conditioning of Least-squares problems |
|
6 |
Systems of Equations • Gaussian elimination and LU factorization • Pivoting and LUP factorization • Stability of Gaussian elimination • Cholesky Factorization |
|
6 |
Eigenvalue Problems • Overview of eigenvalue problems • Reduction to upper-Hessenberg/Tridiagonal form • Power and inverse power iteration • QR algorithm • Computing SVD |
QR_algorithm Computing_SVD |
9 |
Iterative Methods • Arnoldi iteration • GMRES method • Lanczos iteration • Conjugate gradient (CG) method • Jacobi, SOR, and SSOR • Multigrid method |
Arnoldi iterations Arnoldi.htm Krylov_subspace_method2 fine_mesh Multigrid_method |
10 |
Preconditioning Techniques • Introduction • Jacobi, SOR, and SSOR Preconditioners • ILU Factorization Preconditioners • Block Preconditioners |
preconditioning |