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 Free Access
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.
- Kendall Atkinson, Convergence rates for approximate eigenvalues of compact integral operators, SIAM J. Numer. Anal. 12 (1975), 213–222. MR 438746, DOI https://doi.org/10.1137/0712020
- J. H. Bramble and J. E. Osborn, Rate of convergence estimates for nonselfadjoint eigenvalue approximations, Math. Comp. 27 (1973), 525–549. MR 366029, DOI https://doi.org/10.1090/S0025-5718-1973-0366029-9
- Françoise Chatelin, Spectral approximation of linear operators, Computer Science and Applied Mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1983. With a foreword by P. Henrici; With solutions to exercises by Mario Ahués. MR 716134
- Carl de Boor and Blair Swartz, Collocation approximation to eigenvalues of an ordinary differential equation: the principle of the thing, Math. Comp. 35 (1980), no. 151, 679–694. MR 572849, DOI https://doi.org/10.1090/S0025-5718-1980-0572849-1
- David R. Dellwo and Morton B. Friedman, Accelerated spectral analysis of compact operators, SIAM J. Numer. Anal. 21 (1984), no. 6, 1115–1131. MR 765510, DOI https://doi.org/10.1137/0721069
- Jean Descloux, Nabil Nassif, and Jacques Rappaz, On spectral approximation. I. The problem of convergence, RAIRO Anal. Numér. 12 (1978), no. 2, 97–112, iii (English, with French summary). MR 483400, DOI https://doi.org/10.1051/m2an/1978120200971
- Jean Descloux, Nabil Nassif, and Jacques Rappaz, On spectral approximation. I. The problem of convergence, RAIRO Anal. Numér. 12 (1978), no. 2, 97–112, iii (English, with French summary). MR 483400, DOI https://doi.org/10.1051/m2an/1978120200971
- Tosio Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261–322. MR 107819, DOI https://doi.org/10.1007/BF02790238
- M. Thamban Nair, On strongly stable approximations, J. Austral. Math. Soc. Ser. A 52 (1992), no. 2, 251–260. MR 1143193
- William Kolata and John Osborn, Nonselfadjoint spectral approximation and the finite element method, Functional analysis methods in numerical analysis (Proc. Special Session, Annual Meeting, Amer. Math. Soc., St. Louis, Mo., 1977) Lecture Notes in Math., vol. 701, Springer, Berlin, 1979, pp. 115–133. MR 526712
- Gennadi Vainikko, Über die Konvergenz und Divergenz von Näherungsmethoden bei Eigenwertproblemen, Math. Nachr. 78 (1977), 145–164 (German). MR 501887, DOI https://doi.org/10.1002/mana.19770780113
Retrieve articles in Mathematics of Computation 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
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
