# Computational linear algebra

## Summary

This course provides an overview of advanced techniques for solving large-scale linear algebra problems, as they typically arise in applications. A central goal of this course is to give the ability to choose a suitable solver for a given application.

## Content

**Introduction**

Sources of large-scale linear algebra problems. Recap of required linear algebra concepts.

**Eigenvalue problems**

Theory foundations. Krylov subspace methods. Probabilistic analysis. Singular value problems. Preconditioned iterative methods.

**Linear systems**

Direct sparse factorizations. Krylov subspace methods and preconditioners.

**Matrix functions**

Theory and algorithms.

## Keywords

linear systems, eigenvalue problems, matrix functions

## Learning Prerequisites

## Required courses

Linear Algebra, Numerical Analysis

## Learning Outcomes

By the end of the course, the student must be able to:

- Choose method for solving a specific problem.
- Prove the convergence of iterative methods.
- Interpret the results of a computation in the light of theory.
- Implement numerical algorithms.
- Describe methods for solving linear algebra problems.
- State theoretical properties of numerical algorithms.

## Teaching methods

Lectures + exercise sessions

## Expected student activities

Students are expected to attend lectures and participate actively in class and exercises. Exercises will include both theoretical work and programming assignments. Students also complete substantial projects (possibly in small groups) that likewise include theoretical and numerical work.

## Assessment methods

50% of the grade will be based on projects, 50% of the grade will be based on an written exam

## In the programs

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Computational linear algebra**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Computational linear algebra**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Computational linear algebra**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Computational linear algebra**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Computational linear algebra**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Computational linear algebra**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Computational linear algebra**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Computational linear algebra**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Computational linear algebra**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks