Top Eigenpairs of Large Scale Matrices (CSIAM Transactions on Applied Mathematics, 2022)
This paper is devoted to the study of an extended global algorithm on computing the top eigenpairs of a large class of matrices. Three versions of the algorithmare presented that includes a preliminary version for real matrices, one for complexmatrices, and one for large scale sparse real matrix. Some examples are illustrated aspowerful applications of the algorithms. The main contributions of the paper are twolocalized estimation techniques, plus the use of a machine learning inspired approachin terms of a modified power iteration. Based on these new tools, the proposed algorithm successfully employs the inverse iteration with varying shifts (a very fast “cubicalgorithm”) to achieve a superior estimation accuracy and computation efficiency toexisting approaches under the general setup considered in this work.