An Apache Spark Implementation of Block Power Method for Computing Dominant Eigenvalues and Eigenvectors of Large-Scale Matrices

In this paper, we present an implementation of the block power method based on Spark, the big data processing framework, to approximate the dominant eigenvalues and eigenvectors of a large, sparse matrix in distributed computing environment. To take advantage of graph-parallel computation in Spark, we employ the property graph with specially defined vertex and edge types to represent the sparse matrix and the associated block matrix together. Graph operations are then performed on the constructed property graph to efficiently carry out the iteration and decomposition steps of the block power method in parallel. The numerical results on a Markov chain application for modeling stochastic luminal Calcium release site are provided to demonstrate the effectiveness and scalability of the block power method implementation.