Abstract: The leading eigenvalue problems arise in many applications. When the dimension of the matrix is super large, such as for applications in quantum many-body problems, conventional algorithms become impractical due to computational and memory complexity.

In this talk, we will describe some recent works on new approaches for the leading eigenvalue problems based on randomized and coordinate-wise methods. In particular, we will introduce the coordinate-descent full configuration interaction for quantum chemistry problems.
(joint work with Yingzhou Li and Zhe Wang).