Gruppwebben som samarbetsyta stängs 31 december 2026. Du som administratör behöver nu exportera gruppens innehåll och/eller radera gruppen.
Observera: Från och med den 1 oktober 2026 kommer delar av gruppwebben som inte längre används, successivt att stängas ned, exempelvis gruppwebbar som redan har flyttats eller varit inaktiva under en längre tid.
Mer information hittar du i nyheten: Gruppwebben och Social stänger hösten 2026. Stöd och instruktioner för hur du exporterar en gruppwebb finns i: Gruppwebben som samarbetsyta stängs hösten 2026.
Old course overview (HT2016)
Course literature
- Lecture notes in numerical linear algebra (written by the lecturer). PDF-files below.
- Parts from the book "Numerical Linear Algebra", by Lloyd N. Trefethen and David Bau. ISBN: 0-89871-361-7, referred to as [TB]. It is available in Kårbokhandeln. The chapters and recommended pages are specified in the Lecture notes PDF-files.
Course contents:
- Block 1: Large sparse eigenvalue problems
- Literature: eigvals.pdf
- Block 2: Large sparse linear systems
- Literature: linsys.pdf
- Block 3: Dense eigenvalue algorithms (QR-method)
- Literature: qrmethod.pdf
- Block 4: Functions of matrices
- Literature: matrixfunctions.pdf
- Block 5: (only for PhD students taking SF3580) Matrix equations
- Literature: matrixequations.pdf (preliminary)
Learning activities:
The homeworks are mandatory for completion of the course.
- Homework 1. hw1.pdf additional files: arnoldi.m. If homework 1 is completed by deadline (see below) one bonus point is awarded to the exam.
- Homework 2. hw2.pdf. If homework 2 is completed by deadline (see below) one bonus point is awarded to the exam.
- Homework 3. hw3.pdf. You will need alpha_example.m, naive_hessenberg_red.m, and schur_parlett.m. If homework 3 is completed by deadline (see below) one bonus point is awarded to the exam.
- As part of all homeworks: Course training area: wiki. A selection of the exercises suitable for exam preparation are available in selected_exercises.pdf.
Weekly schedule:
Week 1:
- Lecture 1:
- Course introduction: intro_lecture.pdf (username=password=password on wiki)
- Block 1: Basic eigenvalue methods
- Additional video material:
- Lecture 2: Block 1
- Numerical variations of Gram-Schmidt. Arnoldi's method derivation
- Introduction to Arnoldi method: arnoldi_intro.pdf (username=password=password on wiki)
- Numerical variations of Gram-Schmidt orthogonalization
- Lecture 3: Block 1
- Arnoldi's method for eigenvalue problems,
- Intro to convergence of the Arnoldi method for eigenvalue problems
Week 2:
- Lecture 4: Block 1
- Convergence theory for Arnoldi for eigvals continued. Disk reasoning. Shift-and-invert.
- Lanczos method, Lanczos for eigenvalue problems
- Lecture 5:
- Block 2: Iterative methods for linear systems. GMRES derivation
- Deadline HW1
Week 3:
- Lecture 6:
- Block 2: GMRES convergence
- Block 2: Introduction to conjugate gradients (CG method)
- Lecture 7:
- Block 2: Derivation of CG method. Convergence of CG method.
- Lecture 8:
- Block 2: CG-methods for non-symmetric problems: CGN and BiCG
Week 4:
- Lecture 9:
- Block 2: Preconditioning
- Block 3: QR-method intro. Slides: qrmethod_lecture1.pdf
- Lecture 10:
- Block 3: QR-method. Basic QR. Two-phase approach. Improvement 1. Slides: qrmethod_lecture2.pdf
- Deadline HW2
Week 5:
- Lecture 11:
- Block 3: QR-method. Hessenberg QR-method. Slides: qrmethod_lecture3.pdf
- Lecture 12:
- Block 3: QR-method. Acceleration and convergence. qrmethod_lecture4.pdf
Week 6:
- Lecture 13:
- Block 4: Matrix functions. Definitions and basic methods. matrix_functions_lecture1.pdf
- Lecture 14:
- Block 4: Matrix functions. Methods for specialized functions. matrix_functions_lecture2.pdf
- Deadline HW3
Week 7:
- Lecture 15:
- Block 4: Matrix functions. Application to exponential integrators.
