DetaileOld course information 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:

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: qrmethod_lecture1.pdf

https://www.youtube.com/watch?v=qmgxzsWWsNc&feature=youtu.be

* 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

https://people.kth.se/~eliasj/usi_demo_ht16.mp4

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

http://www.math.kth.se/~eliasj/expm_demo1.mp4

Week 7:

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

http://www.math.kth.se/~eliasj/krylov_matfun_sf2524.mp4

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