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   Gopalakrishnan, Jay; Pinochet-Soto, Gabriel (February 2026, Computational Methods in Applied Mathematics)

   Abstract We introduce a framework for repurposing error estimators for sourceproblems to compute an estimator for the gap between eigenspaces and theirdiscretizations. Of interest are eigenspaces of finiteclusters of eigenvalues of unbounded nonselfadjoint linear operatorswith compact resolvent. Eigenspaces and eigenvalues of rationalfunctions of such operators are studied as a first step.Under an assumption of convergence of resolvent approximations inthe operator norm and an assumption on global reliability of sourceproblem error estimators, we show that the gap in eigenspaceapproximations can be bounded by a globally reliable and computableerror estimator. Also included are applications of the theoreticalframework to first-order system least squares(FOSLS) discretizations and discontinuous Petrov–Galerkin (DPG)discretizations, both yielding new estimators for the error gap.Numerical experiments with a selfadjoint model problem and with aleaky nonselfadjoint waveguide eigenproblem show that adaptive algorithmsusing the new estimators give refinement patternsthat target the cluster as a whole instead of individual eigenfunctions. 

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   https://doi.org/10.1145/3133850.3133862  

   Wrenn, John; Krishnamurthi, Shriram (January 2017, International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software)

   This paper presents a lightweight process to guide error report authoring. We take the perspective that error reports are really classifiers of program information. They should therefore be subjected to the same measures as other classifiers (e.g., precision and recall). We formalize this perspective as a process for assessing error reports, describe our application of this process to an actual programming language, and present a preliminary study on the utility of the resulting error reports. 

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