Planned/realized lectures

• week 1 (18-21.1.08): Chapters 1-3
Algebras. Orthogonality, norms.
• week 2 (25-28.1.08): Chapters 4-6
SVD, projectors.
• week 3 (1-4.2.08): Chapters 7-8
QR decompositions (by Gram-Schmidt classical, modified, and Householder).
• week 4 (8-11.2.08): Chapters 10-13
• Least squares, condition.
• flops, accuracy, stability, backward stability.
• week 5 (15-22.2.08): Chapters 14-17
• backward stability of Householder QR
• backward stability of back substitution
• conditioning of the Least Squares problem
• week 6 (25-29.2.08): Chapters 18-21
• stability of Least Squares algorithms
• LU decomposition (Gaussian elimination)
• Pivoting
• week 7 (3-14.3.08): Chapters 22-26
• Stability of LU
• Cholesky decomp.
• Eigenvalues. Jordan, Schur decompositions.
• Reduction to a Hessenberg form
• week 8 (17-28.3.08): Chapters 27-29, 32
• QR iteration
• Overview on iterations
• Classical iterations (Jacobi, Gauss-Seidel, SOR) (not in Trefethen-Bau. See the Eirola-Nevanlinna lecture notes p.76-84)
• week 9 (31.3-4.4.08): Chapters 33, 35, 38
• Arnoldi/Lanczos iterations
• GMRes iteration
• Conjugate Gradient iteration