# 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 a substantial project (possibly in small groups) that likewise include theoretical and numerical work.

## Assessment methods

20% of the grade will be based on projects, 80% of the grade will be based on a 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**Type:**optional

**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**Type:**optional

**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**Type:**optional

**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**Type:**optional

**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**Type:**optional

**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**Type:**optional

**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**Type:**optional

**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**Type:**optional

**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**Type:**optional

**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**Type:**optional

**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**Type:**optional

## Reference week

Mo | Tu | We | Th | Fr | |

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9-10 | |||||

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21-22 |