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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
  • Block 2: Large sparse linear systems
  • Block 3: Dense eigenvalue algorithms (QR-method)
    • Literature: qrmethod.pdf (will be announced later)
  • Block 4: Functions of matrices
  • 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:

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:
  • 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)
  • 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



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