Date | Message |
---|---|
20.12 | The grades for the semester project are now available on itslearning. |
05.12 | Here is the exam and solution: [nor] [eng] [eng sol] |
29.11 | Solution 6 and a temporary version of Solution 5 have been posted. |
28.11 | Important: All students that are taking the course as a specialization course (fordypningsemne), please send me an e-mail confirming this, even if you have informed me about this before. |
27.11 | K. Rottmann: Matematisk formelsamling was added to the list of allowed support material. |
26.11 | Information for those of you that are taking the course as a specialization course has been added to the Exam information. |
26.11 | See Exam information for a list of permitted examination support material for the written exam. |
<schedule> <timeslots>08:15|09:15|10:15|11:15|12:15|13:15|14:15|15:15|16:15</timeslots> <entry day:Mo start:2 end:3 color:ntnu2>Lecture (F3)</entry> <entry day:Mo start:6 end:6 color:ntnu2>Office hour (1301)</entry> <entry day:We start:5 end:6 color:ntnu2>Lecture (F4)</entry> <entry day:We start:7 end:7 color:ntnu2>Exercise (F4)</entry> </schedule>
The exam will test a selection of the Learning outcome.
Permitted examination support material: C: Specified, written and handwritten examination support materials are permitted. A specified, simple calculator is permitted (either Citizen SR-270X or Hewlett Packard HP30S). The permitted examination support materials are:
For those that are taking the course as a specialization course: At the oral exam, you will be presented with a list of three topics. You will then get 5 minutes preparation time. You are allowed to bring the support material listed above to the preparation, but not to the exam itself. In the preparation part, you may take notes on a supplied sheet of paper and bring it with you to the exam. You will then get 45 minutes to present the three topics.
All candidates who are taking the oral exam must meet at 06.12, 09:00 at room 822, Central Building 2. We will then agree upon the candidate order for the exam.
Here is a list of the goals that we will achieve in this course.
S refers to Saad, TB to Trefethen & Bau, GVL to Golub & Van Loan, and R to Rønquist.
Date | Topic | Reference | Learning outcome |
---|---|---|---|
28.10 | QR algorithm with shifts, Wilkinson shift | TB29 | L1.3, L2.4 |
23.10 | QR algorithm without shifts, simultaneous iteration | TB28 | L1.3 |
21.10 | Power iteration, inverse iteration, Rayleigh quotient iteration | TB27 | L1.3 |
16.10 | Eigenvalue problems, eigenvalue-revealing factorizations, eigenvalue algorithms, Rayleigh quotient | TB24–25, TB26 (self-study), TB27 | L1.3, L1.9 |
14.10 | Matrix properties via the SVD | TB5 | L1.9 |
09.10 | DD as a preconditioner, the singular value decomposition (SVD) | GVL2.5, TB4 | L1.9 |
07.10 | MG as a preconditioner in PCG, domain decomposition (DD) methods, Schwarz' alternating procedure, multiplicative and additive overlapping Schwarz | S14.1, S14.3–14.3.3 | L1.8, L2.3 |
02.10 | Intergrid operators, two-grid cycles, V-cycles and W-cycles, red-black Gauss–Seidel | S13.3–13.4.3, S12.4.1 | L1.2, L1.8, L2.3 |
30.09 | Preconditioned CG (PCG), Introduction to multigrid (MG) methods, weighted Jacobi iteration | S9.2.1, S13.1–13.2.2 | L1.2, L1.8 |
25.09 | Convergence of GMRES, complex Chebyshev polynomials, introduction to preconditioning, left-preconditioned GMRES | S6.11.2 (self-study), S6.11.4, S9.1, S9.3.1 | L1.2, L1.7, L1.8 |
23.09 | Convergence of CG, Chebyshev polynomials | S6.11.1, S6.11.3 | L1.6, L2.2 |
18.09 | The D-Lanczos algorithm, the conjugate gradient method (CG) | S6.7.1 | L1.2, L1.6, L2.2, L2.4 |
16.09 | Givens rotations, the Lanczos algorithm, the Lanczos method | S6.5.3, S6.6.1, S6.7.1 | L1.2, L1.6, L1.9 |
11.09 | More on Arnoldi's algorithm, the full orthogonalization method (FOM) and variations of FOM, the generalized minimal residual method (GMRES) | S6.3.1–6.5.1 | L1.2, L1.5, L1.6, L2.2 |
09.09 | Convergence of steepest descent, minimal residual (MR) iteration, convergence of MR, Krylov subspace methods, Arnoldi's algorithm | S5.3.1–5.3.2, S6.1, S6.3–6.3.1 | L1.4, L1.5, L1.6, L2.2 |
04.09 | Projection methods, error projection, residual projection, steepest descent method | S5.1.1–5.2.2, S5.3–5.3.1 | L1.4 |
02.09 | Orthogonal projections, Jacobi - and Gauss–Seidel iteration, convergence of splitting methods, Gershgorin's theorem, the Petrov–Galerkin framework | S1.12.3–1.12.4, S4.1, S4.2–4.2.1, S1.8.4, S4.2.3, S5.1 | L1.1, L1.4 |
28.08 | Perturbation analysis, finite difference methods, diagonalization methods, projection operators | S1.13.1 (self-study), S1.13.2, S2.2–2.2.5 (self-study), R, S1.12.1 | L1.2, L1.4 |
26.08 | Similarity transformations, normal -, Hermitian -, and positive definite matrices | S1.8–1.8.1, S1.8.2 (self-study), S1.8.3, S1.9, S1.11 | L1.9 |
21.08 | QR factorizations | S1.7, TB10 | L1.9 |
19.08 | Background in linear algebra | S1.1–1.3 (self-study), S1.4–1.6 |
The curriculum consists of all topics that have been covered in the lectures, all self-study topics, the semester project, and the exercises with solutions. The lectures and self-study topics are based on the following material. The list is not yet final.
Of the reading material listed below, you should buy the book by Saad, but not necessarily any of the other ones. Saad's book is also available online for free through NTNU's network at SIAM.
The exercises are optional and are not to be handed in. Nevertheless, they are part of the curriculum, and you are encouraged to do them. A new exercise will be posted every one or two weeks.
Solutions will be published one or two weeks after the relevant exercises were published.
The semester project consists of two parts. The first part, which counts for 10 % of the final grade, will be given in September, and the second part, which counts for 20 %, will be given in the end of October/beginning of November. The project is to be done individually or – preferably – in groups of two. Hand in your reports in PDF format and your code by e-mail. You may choose which programming language to use. Please do not type your names on the report, only your candidate numbers. If your candidate number is not available yet, you may use your student number.
Students who are taking the course as a specialization course (fordypningsemne) are not required to do the semester project.
The project will cover learning outcomes L2.1–2.4, and L3.1.
You will need the note Eigenvalues of tridiagonal Toeplitz matrices in the first part of the semester project.