Rump, Siegfried M.Siegfried M.RumpLange, MarkoMarkoLange2023-06-072023-06-072023-12-15Journal of Computational and Applied Mathematics 434: 115332 (2023-12-15)http://hdl.handle.net/11420/15368We present verification methods to compute error bounds for all eigenvectors of a Hermitian matrix as well as for all singular vectors of a rectangular real or complex matrix. In case of clusters these are bounds for an orthonormal basis of the invariant subspace or singular vector space, respectively. Individual error bounds for all eigenvalues and singular values including clustered and/or multiple ones are computed as well. The computed bounds do contain the true result with mathematical certainty, and the algorithms apply to interval data as well. In that case the computed bounds are true for every real/complex matrix within the tolerances. The computational complexity to compute inclusions of all eigen/singular pairs of an n×n matrix or m×n matrix is O(n3) or O(mn2) operations, respectively.en0377-04272023All eigenpairsAll singular pairsHermitian matrixINTLABUnitary matrixVerification methodJournal Article10.1016/j.cam.2023.115332Other