Modul

The module will be completed by an oral exam (ca. 20  min).

The students have basic knowledge of the approximation of functions of operators. They can examine the methods for convergence properties and efficiency. In the context of semigroups, they can analyze the procedures discussed, independently select the appropriate procedures and justify their choice.

None

• Definition of functions of operators
• Strongly continuous and analytic semigroups
• Rational approximations to functions of operators with fixed poles
• Rational Krylov subspace method for the approximation of functions of operators
• Applications in the numerical analysis of semigroups

The courses Numerical Analysis 1 and 2, and Functional Analysis are strongly recommended.

Total workload: 180 hours

Attendance: 60 hours

• lectures, problem classes, and examination

Self-studies: 120 hours

• follow-up and deepening of the course content,
• work on problem sheets,
• literature study and internet research relating to the course content,
• preparation for the module examination