Hochstenbach, Michiel E.; Plestenjak, Bor Computing several eigenvalues of nonlinear eigenvalue problems by selection. (English) Zbl 1439.65045 Calcolo 57, No. 2, Paper No. 16, 25 p. (2020). Several selection criteria for computing eigenvalues for nonlinear one-parameter and linear and nonlinear multi-parameter eigenvalue problems are given. Remarkably, in the case of nonlinear problems, the methods work directly on the original problem and linearizations are not needed.The approach can be successfully applied to general nonlinear eigenproblems. Reviewer: Anton Iliev (Plovdiv) Cited in 4 Documents MSC: 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 65F50 Computational methods for sparse matrices 65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems 15A18 Eigenvalues, singular values, and eigenvectors 15A69 Multilinear algebra, tensor calculus Keywords:eigenvalues; selection; divided difference; deflation; locking; homogeneous coordinates; polynomial eigenvalue problem; nonlinear eigenvalue problem; multiparameter eigenvalue problem; subspace method Software:quadeig; MultiParEig; NLEVP PDFBibTeX XMLCite \textit{M. E. Hochstenbach} and \textit{B. Plestenjak}, Calcolo 57, No. 2, Paper No. 16, 25 p. (2020; Zbl 1439.65045) Full Text: DOI arXiv References: [1] Bai, Z.; Su, Y., SOAR: a second-order Arnoldi method for the solution of the quadratic eigenvalue problem, SIAM J. Matrix Anal. 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