Numerical Methods for Nonlinear Equations
Additional Info
- ECTS credits: 5
- University: Leibniz University Hannover
- Semester: 2
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Topics:
In the class “Numerical Methods for Nonlinear Equations,” we discuss the treatment of nonlinear problems in general Banach spaces(finite and infinite dimensional). We examine convergence properties of general iterative methods and apply these principles to specific iterative methods, such as Newton's method.
The course includes a thorough convergence analysis of Newton's method and explores various Newton-type methods. Typically, the iterative methods covered provide a single solution to a given problem. However, the deflation method can be employed to obtain multiple solutions.
Additionally, for challenging but smooth nonlinear problems, continuation methods (homotopy methods) can be used to find solutions. These methods are also part of the lecture content.
