Efficient Iterative Methods for Fast Solution of Integral Operators Related Problems


The discretization of integral operator related problems inevitably leads to some kind of linear system involving dense matrices. Such large scale systems can be prohibitively expensive to solve.


Boundary Integral Equation Helmholtz Equation Wavelet Method Blind Deconvolution Fast Multipole Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AmPr99]
    Amini, S., Profit, A.J.: Analysis of a diagonal form of the fast multipole algorithm for scattering theory. BIT, 39, 585–602 (1999). MathSciNetzbMATHCrossRefGoogle Scholar
  2. [AmHaWi92]
    Amini, S., Harris, P.J., Wilton, D.T.: Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-Structure Interaction Problem, Lecture Note in Engineering, 77, C.A. Brebbia and S.A. Orszag, eds., Springer, London (1992). Google Scholar
  3. [Ba08]
    Banjai, L., Hackbusch, W.: Hierarchical matrix techniques for low and high frequency Helmholtz equation. IMA J. Numer. Anal., 28, 46–79 (2008). MathSciNetzbMATHCrossRefGoogle Scholar
  4. [BrGr97]
    Beatson, R., Greengard, L.: A short course on fast multipole methods, in Wavelets, Multilevel Methods and Elliptic PDEs, Oxford University Press, 1–37 (1997). See also Google Scholar
  5. [BrCh10]
    Brito, C., Chen, K.: Multigrid algorithm for high order denoising. SIAM J. Imaging Sci., 3, 363–389 (2010). MathSciNetzbMATHCrossRefGoogle Scholar
  6. [ChCh10]
    Chan, R.H., Chen, K.: A multilevel algorithm for simultaneously denoising and deblurring images. SIAM J. Sci. Comput., 32, 1043–1063 (2010). MathSciNetzbMATHCrossRefGoogle Scholar
  7. [ChCh02]
    Chan, T.F., Chen, K.: On two variants of an algebraic wavelet preconditioner. SIAM J. Sci. Comput., 24, 260–283 (2002). MathSciNetzbMATHCrossRefGoogle Scholar
  8. [ChSh05]
    Chan, T.F., Shen, J.H.: Image Processing and Analysis – Variational, PDE, Wavelet, and Stochastic Methods, SIAM Publications (2005). zbMATHGoogle Scholar
  9. [ChWo98]
    Chan, T.F., Wong, C.K.: Total variation blind deconvolution. IEEE Trans. Image Process, 7, 370–375 (1998). CrossRefGoogle Scholar
  10. [Ch05]
    Chen, K.: Matrix Preconditioning Techniques and Applications, Cambridge University Press, Cambridge (2005). zbMATHCrossRefGoogle Scholar
  11. [Ci00]
    Cipra, B.A.: The Best of the 20th Century: Editors Name Top 10 Algorithms. SIAM News, 33 (2000). Google Scholar
  12. [Da97]
    Dahmen, W.: Wavelet and multiscale methods for operator equations. Acta Numerica, 1997, 55–228 (1997). Google Scholar
  13. [Fo09]
    Fong, W., Darve, E.: The black-box fast multipole method. J. Comp. Phys., 228, 8712–8725 (2009). MathSciNetzbMATHCrossRefGoogle Scholar
  14. [HaCh05]
    Hawkins, S., Chen, K.: An implicit wavelet approximate inverse preconditioner. SIAM J. Sci. Comput., 27, 667–686 (2005). MathSciNetzbMATHCrossRefGoogle Scholar
  15. [HuNgWe08]
    Huang, Y., Ng, M., Wen, Y.: A fast total variation minimization method for image restoration. SIAM J. Multiscale Modeling and Simulation, 7, 774–795 (2008). MathSciNetzbMATHCrossRefGoogle Scholar
  16. [MaSc07]
    Mazya, V., Schmidt, G.: Approximate Approximations, American Mathematical Society, Providence, RI (2007). Google Scholar
  17. [MoKa08]
    Money, J.H., Kang, S.H.: Total variation minimizing blind deconvolution with shock filter. Image Vision Comput., 26, 302–314 (2008). CrossRefGoogle Scholar
  18. [NgBo03]
    Ng, M., Bose, N.K.: Mathematical analysis of super-resolution methodology. IEEE Signal Proc. Magazine, 20, 62–74 (2003). CrossRefGoogle Scholar
  19. [RuOsFa92]
    Rudin, L.I., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D, 60, 259–268 (1992). zbMATHCrossRefGoogle Scholar
  20. [SaSc96]
    Saad, Y., Schultz, M.H.: GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7, 856–869 (1986). MathSciNetzbMATHCrossRefGoogle Scholar
  21. [TrOoSc2001]
    Trottenberg, U., Oosterlee, C., Schuller, A.: Multigrid, Academic Press (2001). zbMATHGoogle Scholar
  22. [Vo02]
    Vogel, C.R.: Computational Methods for Inverse Problems, SIAM Publications, Philadelphia, PA (2002). zbMATHCrossRefGoogle Scholar
  23. [WaYaYihZ08]
    Wang, Y., Yang, J., Yin, W., Zhang, Y.: A new alternating minimization algorithm for total variation image reconstruction. SIAM J. Imaging Sci., 1, 248–272 (2008). MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of LiverpoolLiverpoolUK

Personalised recommendations