Old course 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
  • Block 2: Large sparse linear systems
  • Block 3: Dense eigenvalue algorithms (QR-method)
  • Block 4: Functions of matrices
  • Block 5: (only for PhD students taking SF3580) Matrix equations

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:
  • 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

Week 2:

  • Lecture 4: Block 1
    • Convergence theory for Arnoldi for eigvals continued. Disk reasoning. Shift-and-invert.
    • 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
    • Block 2: Introduction to conjugate gradients (CG method)
  • Lecture 7:
    • Block 2: Derivation of CG method. Convergence of CG method.
  • Lecture 8:
    • Block 2: CG-methods for non-symmetric problems: CGN and BiCG

Week 4:

  • Lecture 10:
    • Block 3: QR-method. Basic QR. Two-phase approach. Improvement 1. Slides: qrmethod_lecture2.pdf
    • Deadline HW2

Week 5:

Week 6:

Week 7:

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

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