Research

My current research work is focused on the following computational problems for large scale matrices. 

 

• Preocnditioned Krylov subspace methods for computing eigenvalues of large matrices. Developing Krylov subspace methods that can be accelerated efficiently by some equivalent transformations (preconditioning) is a grand challenge in the eigenvalue computations.
• Finite precision analysis of  Krylov subspace methods for solving linear systems A x = b. Many elegant Krylov subspace methods have been developed in the last decade for nonsymmetric linear systems, but they may become unstable in finite precision. Our goal is to understand the effect of rounding errors in these algorithms so as to develop methods to improve their stability. 
• High relative accuracy computations and applications. We study when and how some tiny quantities (e.g. tiny eigenvalues) are determined and hence can be computed to high relative accuracy. Applications in stochastic models are part of our study.  

My research interest also includes some other problems in linear algebra, operator theory and engineering applications.