In usual synchronous parallel computing, workload balance is a crucial factor to reduce idle times of some processors that have finished their jobs earlier than others. However, it is difficult to achieve on a heterogeneous workstation clusters where the available computing power of each processor is unpredictable. As a way to overcome such a problem, the idea of asynchronous methods has grown out and is being increasingly used and studied, but there is none for eigenvalue problems yet. In this paper, we suggest a new asynchronous method to solve some singular matrix problems, that can also be used for finding a certain eigenvector of some matrices.