Numerical computations for long-wave short-wave interaction equations in semi-classical limit
This work is devoted to the study of the production and benchmarking of several refinements of the power method that enable the computation of multiple extremal eigenpairs of very large matrices. The authors used an observation by Booth in these refinements, that has made possible the calculation of up to the 10th eigenpair for simple test problems, simulating the transport of neutrons in the steady state of a nuclear reactor. In this manuscript the authors summarize their techniques and efforts to-date on determining mainly just the two largest or two smallest eigenpairs. To illustrate the effectiveness of the techniques, they determined the two extremal eigenpairs of a cyclic matrix, the transfer matrix of the two-dimensional Ising model, and the Hamiltonian matrix of the one-dimensional Hubbard model.
scientific article; zbMATH DE number 5349705
scientific article