Detailed course information

This page is under construction. More information will be announced here later. In the meantime you can also see the information in the  course pages of previous year.

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: sparse_eig.pdf (will be announced later)
• Block 2: Large sparse linear systems
  • Literature: linsys.pdf (preliminary)
• Block 3: Dense eigenvalue algorithms (QR-method)
  • Literature: qrmethod.pdf (will be announced later)
• 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:

• Homework 1. hw1.pdf additional files: arnoldi.m
• Homework 2 (will appear later)
• Homework 3 (will appear later)
• As part of all homeworks: Course training area: wiki. Mobile devices can use QR-code:

Weekly schedule:

Week 1:

• Lecture 1:
  • Course introduction
  • Block 1: Basic eigenvalue methods
  • Additional video material:

• Lecture 2:
  • Block 1: Numerical variations of Gram-Schmidt. Arnoldi's method derivation

• Lecture 3:
  • Block 1: Arnoldi's method for eigenvalue problems, shift-and-invert

Week 2:

• Lecture 4:
  • Block 1: 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
• Lecture 7:
  • Block 2: CG-method

• Lecture 8:
  • Block 2: CG-methods for non-symmetric problems

Week 4:

• Lecture 9:
  • Block 2: Preconditioning
  • Deadline HW2
• Lecture 10:
  • Block 3: QR-method. Basic QR. Two-phase approach.

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

Week 7:

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