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On spectral approximation. Part 1. The problem of convergence. (English) Zbl 0393.65024

MSC:
65J10 Numerical solutions to equations with linear operators (do not use 65Fxx)
47A10 Spectrum, resolvent
35P15 Estimates of eigenvalues in context of PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
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References:
[1] 1. P. M. ANSELONE, Collectively Compact Operator Approximation theory, Prentice-Hall, 1971. Zbl0228.47001 MR443383 · Zbl 0228.47001
[2] 2. J. DESCLOUX, Two Basic Properties of Finite Elements, Rapport, Département de Mathématiques, E.P.F.L., 1973.
[3] 3. J. DESCLOUX, N. NASSIF and J. RAPPAZ, Spectral Approximations with Error Bounds for Non Compact Operators, Rapport, Département de Mathématiques, E.P.F.L., 1977.
[4] 4. J. DESCLOUX, N. NASSIF and J. RAPPAZ, Various Results on Spectral Approximation, Rapport, Département de Mathématiques, E.P.F.L., 1977. · Zbl 0361.65052
[5] 5. T. KATO, Perturbation Theory of Linear Operators, Springer-Verlag, 1966. Zbl0148.12601 MR203473 · Zbl 0148.12601
[6] 6. J. NITSCHE and A. SCHATZ, On Local Approximation properties of L2-Projection on Spline-Subspaces, Applicable analysis, Vol. 2, 1972, pp. 161-168. Zbl0239.41007 MR397268 · Zbl 0239.41007 · doi:10.1080/00036817208839035
[7] 7. J. RAPPAZ, Approximation of the Spectrum of a Non-Compact Operator Given by the Magnetohydrodynamic Stability of a Plasma, Numer. Math., Vol. 28, 1977, pp. 15-24. Zbl0341.65044 MR474800 · Zbl 0341.65044 · doi:10.1007/BF01403854 · eudml:132472
[8] 8. F. RIESZ and B. Z. NAGY, Leçons d’analyse fonctionnelle, Gauthier-Villars, Paris, 6e éd., 1972. Zbl0064.35404 · Zbl 0064.35404
[9] 9. G. M. VAINIKKO, The Compact Approximation Principle in the Theory of Approximation Methods, U.S.S.R. Computational Mathematics and Mathematical Physics, Vol. 9, No. 4, 1969, pp. 1-32. Zbl0236.65038 MR257771 · Zbl 0236.65038 · doi:10.1016/0041-5553(69)90031-7
[10] 10. G. M. VAINIKKO, A Difference Method for Ordinary Differential Equations,U.S.S.R. Computational Mathematics and Mathematical Physics, Vol. 9,No. 5, 1969. Zbl0233.34021 MR280027 · Zbl 0233.34021 · doi:10.1016/0041-5553(69)90156-6
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