期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2008
卷号：105
期号：22
页码：7631-7635
DOI：10.1073/pnas.0801047105
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Many fields of science and engineering require finding eigenvalues and eigenvectors of large matrices. The solutions can represent oscillatory modes of a bridge, a violin, the disposition of electrons around an atom or molecule, the acoustic modes of a concert hall, or hundreds of other physical quantities. Often only the few eigenpairs with the lowest or highest frequency (extremal solutions) are needed. Methods that have been developed over the past 60 years to solve such problems include the Lanczos algorithm, Jacobi-Davidson techniques, and the conjugate gradient method. Here, we present a way to solve the extremal eigenvalue/eigenvector problem, turning it into a nonlinear classical mechanical system with a modified Lagrangian constraint. The constraint induces exponential inflationary growth of the desired extremal solutions.
