Fully computable a posteriori error estimates for eigenfunctions of compact self-adjoint operators in Hilbert spaces are derived. The problem of ill-conditioning of eigenfunctions in case of tight clusters and multiple eigenvalues is solved by estimating the directed distance between the spaces of exact and approximate eigenfunctions. Derived upper bounds apply to various types of eigenvalue problems, e.g. to the (generalized) matrix, Laplace, and Steklov eigenvalue problems. These bounds are suitable for arbitrary conforming approximations of eigenfunctions, and they are fully computable in terms of approximate eigenfunctions and two-sided bounds of eigenvalues. Numerical examples illustrate the efficiency of the derived error bounds for eigenfunctions.

翻译：完全可计算Hilbert空间内紧凑自合操作器机能的事后误差估计数; 计算出在紧凑组群和多种源值情况下对机能的失灵问题,通过估计精确和近似源值空间之间的直接距离来解决。 衍生上界适用于各种类型的机能问题,例如(通用)矩阵、 Laplace 和 Steklov 机能问题。这些边框适合于任意符合机能近似值的情况,而且就机能的近似值和电子值的两面界限而言,这些边框完全可计算。