Local two-sided bounds for eigenvalues of self-adjoint operators
The authors examine the equivalence between two numerical methods for computing local two-sided bounds for eigenvalues of self-adjoint operators. The first, developed by \textit{S. Zimmermann} and \textit{U. Mertins} [Z. Anal. Anwend. 14, No. 2, 327--345 (1995; Zbl 0831.35117)], is based on ideas of N. J. Lehmann, H. J. Maehly, and F. Goerische, while the second is a geometrically motivated method of \textit{E. B. Davies} and \textit{M. Plum} [IMA J. Numer. Anal. 24, No. 3, 417--438 (2004; Zbl 1062.65056)]. The authors establish a general framework allowing the sharpening of previously known results, they determine explicit convergence estimates, and they use a resonant cavity problem that they studied earlier [SIAM J. Sci. Comput. 36, No. 6, A2887--A2906 (2014; Zbl 1317.78012)] to demonstrate the applicability of the Zimmermann-Mertins method [loc. cit.].
scientific article; zbMATH DE number 6705753
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