Numerical Linear Algebra

Teaching semester

Autumn

Objectives and Content

This course deals with algorithms to solve: The eigenvalue problem superdeterminant equation systems and linear equation systems (onlyKrylov subspace iteration). Algorithms for matrix decomposition as QR-factorisation and Singular-value decomposition will be discussed and analysed with respect to stability and complexity.

Learning Outcomes

Upon completion of the course, the successful candidate shall be able to:

• Choose the most appropriate numerical method to solve a given linear algebra problem.
• Explain and describe the principles of SVD, QR, LU and Cholesky factorization of matrices.
• Have the knowledge of different methods for eigenvalue problems, like power method, divide and conquer and QR method.
• Explain the principles of Krylov subspace methods, like the Arnoldi iteration, GMRES, Lanczos iteration and conjugate gradients.
• Analyze the speed and rate of convergence and stability of numerical algorithms.

Required Previous Knowledge

None

Recommended Previous Knowledge

MAT160 Scientific computing I

Credit Reduction due to Course Overlap

INF261: 10 ECTS

Compulsory Assignments and Attendance

Exercises.

Forms of Assessment

Oral exam. Exercises might be graded and included in the final grade.

Grading Scale

The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.