Multi-level iteration methods for solving integral equations of the second kind

Journal of Integral Equations and Applications

Volumn 14, Issue 4, 2002, Pages 355-376

  Fang, Weifu ^a   Ma, Fuming ^b   Xu, Yuesheng ^a,c  

^a WEST VIRGINIA UNIVERSITY   (United States)

^b JILIN UNIVERSITY   (China)

^c CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Fredholm integral equations; Multi level iteration methods; Multi resolution analysis

Indexed keywords

EID: 1842722770     PISSN: 08973962     EISSN: None     Source Type: Journal    
DOI: 10.1216/jiea/1181074928     Document Type: Article

References (17)

1. 2 for the sparse representation of integral operator, SIAM J. Math. Anal. 24 (1993), 246-262.
2. K.E. Atkinson, The numerical solution of integral equations of second kind, Cambridge Univ. Press, Cambridge, 1997.
3. 3, SIAM J. Sci. Stat. Comp. 15 (1994), 1083-1104.
4. G. Beylkin, R.R. Coifman and V. Rokhlin, Fast wavelet transforms and numerical algorithms I, Comm. Pure Appl. Math. 44 (1991), 141-183.
5. Z. Chen, C.A. Micchelli and Y. Xu, A multilevel method for solving operator equations, J. Math. Anal. Appl. 262 (2001), 688-699.
6. Z. Chen, The Petrov-Galerkin methods for second kind integral equations II: Multiwavelet scheme, Adv. Comp. Math. 7 (1997), 199-233.
7. Z. Chen, A construction of interpolating wavelets on invariant sets, Comp. Math. 68 (1999), 1560-1587.
8. Z. Chen, Discrete wavelet Petrov-Galerkin methods, Adv. Comp. Math. 16 (2002), 1-28.
9. Z. Chen, Fast collocation method for second kind integral equations, SIAM J. Numer. Anal. 40 (2002), 344-375.
10. Z. Chen, B. Wu and Y. Xu, Fast solutions of discrete linear systems resulted from multiscale methods for solving operator equations, preprint, 2001.
11. W. Dahmen, Wavelet and multiscale methods for operator equations, Acta Numerica (1997), 55-228.
12. W. Dahmen, S. Proessdorf and R. Schneider, Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solutions, Adv. Comput. Math. 1 (1993), 259-335.
13. W. Hackbusch, Multi-grid methods and applications, Springer-Verlag, Berlin, 1986.
14. R. Kress, Linear integral equations, 2nd ed., Springer-Verlag, New York, 1999.
15. C.A. Micchelli and Y. Xu, Using the matrix refinement equation for the construction of wavelets on invariant sets, Appl. Comput. Harmon. Anal. 1 (1994), 391-401.
16. C. A. Micchelli, Y. Xu and Y. Zhao, Wavelet Galerkin methods for secondkind integral equations, J. Comput. Appl. Math. 86 (1997), 251-270.
17. T. von Petersdorff, C. Schwab and R. Schneider, Multiwavelets for secondkind integral equations, SIAM J. Numer. Anal. 34 (1997), 2212-2227.