A Contour-integral Based Method for Generalized Eigenvalue Problems
Speaker Dr. Guojian Yin
Hong Kong University of Science and Technology
About the Speaker
Dr. Yin received his PhD degree in mathematics from the Chinese University of Hong Kong. He is now a postdoctoral fellow at the Hong Kong University of Science and Technology. Dr. Yin’s research interests include developing efficient algorithms for large-scale eigenvalue problems, low-rank matrix/Tensor completion and RPCA, machine learning, etc.
The contour-integral based eigensolvers are the recent efforts for computing the eigenvalues inside a given region in the complex plane. The best-known members are the Sakurai-Sugiura (SS) method, and the FEAST algorithm. An attractive computational advantage of these methods is that they are easily parallelizable. The FEAST algorithm was developed for the generalized Hermitian eigenvalue problems. It is stable and accurate. However, it may fail when applied to non-Hermitian problems. In this talk, we will introduce a generalized FEAST algorithm, which aims to extend FEAST to the non-Hermitian problems. Our approach can be summarized as follows: (i) construct a particular contour integral to form a search subspace containing the desired eigenspace, and (ii) use the oblique projection technique to extract desired eigenpairs with appropriately chosen test subspace. In addition, in the talk, a contour-integral based method for counting the eigenvalues inside a given region will be introduced.
All are welcome！