## Numerical methods for spectral problems: theory and applications

P000021

### Rigorous and fully computable a posteriori error bounds for eigenfunctions

Xuefeng Liu (Niigata University)
*Tomas Vejchodsky (Institute of Mathematics, Czech Academy of Sciences)

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 Related papers [1] G. Birkhoff, C. De Boor, B. Swartz, B. Wendroff: Rayleigh-Ritz approximation by piecewise cubic polynomials, SIAM J. Numer. Anal. 3 (1966), no. 2, 188--203. [2] E. Canc\es, G. Dusson, Y. Maday, B. Stamm, M. Vohral{\'\i}k: Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: conforming approximations. SIAM J. Numer. Anal. 55 (2017), no. 5, 2228--2254. [3] E. Canc\es, G. Dusson, Y. Maday, B. Stamm, M. Vohral{\'\i}k: Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: a unified framework. Numer. Math. 140 (2018), no. 4, 1033--1079. [4] E. Canc\`es, G. Dusson, Y. Maday, B. Stamm, M. Vohral{\'\i}k: Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors: multiplicities and clusters. In preparation (2019). [5] X. Liu, T. Vejchodsk\'y: Rigorous and fully computable a posteriori error bounds for eigenfunctions. Preprint arXiv:1904.07903 (2019). Keywords Laplace, eigenvalue problem, guaranteed, rigorous, error estimation, eigenfunction, multiple, cluster, directed distance, gap, finite element method