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 (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