Faculty Research Perspectives

Convergence of iterative methods for nearly singular problems

Young-Ju Lee

March 31, 3:30 PM in Hill 705



Abstract.

I will discuss the solution by iterative methods for a nearly singular system of equations. By taking simple examples, we illustrate that classical iterative methods like Jacobi or Gauss-Seidel method can be very inefficient for nearly singular problems while they could be efficient for limiting problems, which would be singular or non invertible. To tackle these difficulties in a simple example, we provide a simple remedy, which makes the encountered difficulty disappear. It turns out that this remedy can be formulated as a general guide from which robust iterative method can be devised for many important nearly singular problems. The main motivation for this research comes from mathematical models in fluid dynamics.

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