## Numerical methods for spectral problems: theory and applications

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### Some high-efficiency algorithms for eigenvalue problems

*Shuo Zhang (Institute of Computational Mathematics, Chinese Academy of Sciences)

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 Related papers Z., Y. Xi, X. Ji, A multi-level mixed element method for the eigenvalue problem of biharmonic equation, Journal of Scientific Computing, 75(2018), 1415--1444. Y. Xi, X. Ji, Z., A multi-level mixed element scheme of the two dimensional Helmholtz transmission eigenvalue problem, IMA J. Numer. Anal., online. Z., Optimal piecewise cubic finite element schemes for the biharmonic equation on general triangulations. submitted. available as arXiv preprint: 1903.04897 Keywords eigenvalue problem; high-efficiency algorithm; multigrid algorithm; upper/lower bounds; nonstandard phenomena