Detailed course information

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 (preliminary)

* 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. Mobile devices can use QR-code:
qr

Weekly schedule: Week 1:

* Lecture 1:
* Course introduction: intro_lecture.pdf (username=password=password on wiki)
* Block 1: Basic eigenvalue methods
* Additional video material:

https://people.kth.se/~eliasj/power_method_ht16.mp4

* 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

https://people.kth.se/~eliasj/arnoldi_eig1.mp4

Week 2:

* Lecture 4: Block 1
* Convergence theory for Arnoldi for eigvals continued. Disk reasoning. Shift-and-invert.
* Lanczos method, Lanczos for eigenvalue problems

https://people.kth.se/~eliasj/lanczos_method_derivation.mp4

* 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.

https://people.kth.se/~eliasj/cg_demo_ht16.mp4

* Lecture 8:
* Block 2: CG-methods for non-symmetric problems: CGN and BiCG

https://people.kth.se/~eliasj/cgne_demo_ht16.mp4

Week 4:

* Lecture 9:
* Block 2: Preconditioning
* Block 3: QR-method intro. Slides (PDF)

* Lecture 10:
* Block 3: QR-method. Basic QR. Two-phase approach. Improvement 1. Slides (PDF)
* Deadline HW2

Week 5:

* Lecture 11:
* Block 3: QR-method. Hessenberg QR-method

* Lecture 12:
* Block 3: QR-method. Acceleration and convergence

Week 6:

* Lecture 13:
* Block 4: Matrix functions. Definitions and basic methods.

* Lecture 14:
* Block 4: Matrix functions. Methods for specialized functions
* Deadline HW3

Week 7:

* Lecture 15:
* Block 4: Matrix functions. Application to exponential integrators.
* Short course summary

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