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

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 