Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Accelerated spectral approximation


Authors: Rafikul Alam, Rekha P. Kulkarni and Balmohan V. Limaye
Journal: Math. Comp. 67 (1998), 1401-1422
MSC (1991): Primary 47A10, 47A58, 47A75, 65B99, 65J99
DOI: https://doi.org/10.1090/S0025-5718-98-00980-6
MathSciNet review: 1484895
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A systematic development of higher order spectral analysis, introduced by Dellwo and Friedman, is undertaken in the framework of an appropriate product space. Accelerated analogues of Osborn's results about spectral approximation are presented. Numerical examples are given by considering an integral operator.


References [Enhancements On Off] (What's this?)

  • 1. K. ATKINSON, Convergence rates for approximate eigenvalues of compact operators, SIAM J. Numer. Anal., 12(1975), pp 213 - 222. MR 55:11653
  • 2. J. H. BRAMBLE AND J. E. OSBORN, Rate of convergence estimates of nonselfadjoint eigenvalue problem, Math. Comp., 27(1973), pp 525 - 549. MR 51:2280
  • 3. F. CHATELIN, Spectral Approximation of Linear Operators, Academic Press, New York (1983). MR 86d:65071
  • 4. C. DE BOOR AND B. SWARTZ, Collocation approximation to eigenvalues of an ordinary differential equation: The principle of the thing, Math. Comp., 35(1980), pp. 679 - 694. MR 81k:65097
  • 5. D. DELLWO AND M.B. FRIEDMAN, Accelerated spectral analysis of compact operators, SIAM J. Numer. Anal., 21(1984), pp 1115 - 1131. MR 86b:65059
  • 6. J. DESCLOUX, N. NASSIF AND J. RAPPAZ, On spectral approximation. Part 1. The problem of convergence, R.A.I.R.O. Numer. Anal., 12(1978), pp. 97 - 112. MR 58:3404a
  • 7. J. DESCLOUX, N. NASSIF AND J. RAPPAZ, On spectral approximation. Part 2. Error estimates for the Galerkin method, R.A.I.R.O. Numer. Anal., 12(1978), pp. 113 - 119. MR 58:3404b
  • 8. T. KATO, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math., 6(1958), pp. 261 - 232. MR 21:6541
  • 9. M. T. NAIR, On strongly stable approximations, J. Austral. Math. Soc. (Series A), 52(1992), pp. 251 - 260. MR 92k:47034
  • 10. J. E. OSBORN, Spectral approximation for compact operators, Math. Comp., 29(1975), pp 712-725. MR 81f:65041
  • 11. G. VAINIKKO, Uber die Konvergenz und Divergenz von Näherungsmethoden bei Eigenwertproblemen, Math. Nachr., 78(1977), pp. 145 - 164. MR 58:19122a

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 47A10, 47A58, 47A75, 65B99, 65J99

Retrieve articles in all journals with MSC (1991): 47A10, 47A58, 47A75, 65B99, 65J99


Additional Information

Rafikul Alam
Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, India
Address at time of publication: Department of Mathematics, Indian Institute of Technology Guwahati, India
Email: rafik@iitg.ernet.in

Rekha P. Kulkarni
Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, India
Email: rpk@math.iitb.ernet.in

Balmohan V. Limaye
Affiliation: Department of Mathematics, Indian Institute of Technology Bombay, India
Email: bvl@math.iitb.ernet.in

DOI: https://doi.org/10.1090/S0025-5718-98-00980-6
Keywords: Spectral approximation, higher order spectral analysis, eigenvalue of finite algebraic multiplicity, spectral projection, spectral subspace, eigenvector
Received by editor(s): September 11, 1995
Received by editor(s) in revised form: October 30, 1996
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society