[1]
|
D. De Leon, “A New Wavelet Multigrid Method,” Journal of Computational and Applied Mathematics, Vol. 220, No. 1-2, 2008, pp. 674-675.
doi:10.1016/j.cam.2007.09.021
|
[2]
|
B. Engquist and E. Luo, “The Multigrid Method Based on a Wavelet Transformation and Schur Complement,” Unpublished.
|
[3]
|
D. De Leon, “Wavelet Operators Applied to Multigrid Methods,” Ph.D. Thesis, UCLA, Los Angeles, 2000.
|
[4]
|
W. L. Briggs and V. E. Henson, “Wavelets and Multigrid,” SIAM Journal on Scientific Computing, Vol. 14, No. 2, 1993, pp. 506-510. doi:10.1137/0914031
|
[5]
|
M. Dorobantu and B. Engquist, “Wavelet-Based Numerical Homogenization,” SIAM Journal on Numerical Analysis, Vol. 35, No. 2, 1998, pp. 540-559.
doi:10.1137/S0036142996298880
|
[6]
|
B. Engquist and E. Luo, “New Coarse Grid Operators for Highly Oscillatory Coefficient Elliptic Problems,” Journal of Computational Physics, Vol. 129, No. 2, 1996, pp. 296-306. doi:10.1006/jcph.1996.0251
|
[7]
|
B. Engquist and E. Luo, “Convergence of a Multigrid Method for Elliptic Equations with Highly Oscillatory Coefficients,” SIAM Journal on Numerical Analysis, Vol. 34, No. 6, 1997, pp. 2254-2273.
doi:10.1137/S0036142995289408
|
[8]
|
N. Neuss, W. Jager and G. Wittum, “Homogenization and Multigrid,” Computing, Vol. 66, No. 1, 2001, pp. 1-26.
doi:10.1007/s006070170036
|
[9]
|
J. D. Moulton, J. E. Dendy, Jr. and J. M. Hyman, “The Black Box Multigrid Numerical Homogenization Algorithm,” Journal of Computational Physics, Vol. 142, No. 1, 1998, pp. 80-108. doi:10.1006/jcph.1998.5911
|
[10]
|
P. J. Van Fleet, “Discrete Wavelet Transformations: An Elementary Approach with Applications,” Wiley-Interscience, Hoboken, 2008. doi:10.1002/9781118032404
|
[11]
|
X. Yang, Y. Shi and B. Yang, “General Framework of the Construction of Biorthogonal Wavelets Based on Bernstein Bases: Theory Analysis and Application in Image Compression,” IET Computer Vision, Vol. 5, No. 1, 2011, pp. 50-67. doi:10.1049/iet-cvi.2009.0083
|
[12]
|
W. Sweldens, “The Lifting Scheme: A Construction of Second Generation Wavelets,” SIAM Journal on Mathematical Analysis, Vol. 29, No. 2, 1997, pp. 511-546.
doi:10.1137/S0036141095289051
|
[13]
|
D. Taubman and M. Marcellin, “JPEG2000: Image Compression Fundamentals, Standards and Practice,” The International Series in Engineering and Computer Science, Kluwer Academic, Norwell, 2002.
|
[14]
|
S. Dahlke and A. Kunoth, “Biorthogonal Wavelets and Multigrid,” In Adaptive Methods: Algorithms, Theory and Applications, Proceedings of the 9th GAMM Seminar, Kiel, 1993, pp. 99-119.
|
[15]
|
L. Cheng, H. Wang and Z. Zhang, “The Solution of Ill-Conditioned Symmetric Toeplitz Systems via Two-Grid and Wavelet Methods,” Computers and Mathematics with Applications, Vol. 46, No. 5-6, 2003, pp. 793-804.
doi:10.1016/S0898-1221(03)90142-8
|
[16]
|
A. P. Reddy and N. M. Bujurke, “Biorthogonal Wavelet Based Algebraic Multigrid Preconditioners for Large Sparse Linear Systems,” Applied Mathematics, Vol. 2, No. 11, 2011, pp. 1378-1381. doi:10.4236/am.2011.211194
|
[17]
|
W. L. Briggs, S. F. McCormick and V. E. Henson, “A Multigrid Tutorial,” 2nd Edition, SIAM, Philadelphia, 2000.
doi:10.1137/1.9780898719505
|
[18]
|
S. McCormick, Ed., “Multigrid Methods,” Frontiers in Applied Mathematics, SIAM, Philadelphia, 1987.
|
[19]
|
U. Trottenberg, C. W. Oosterlee and A. Schüller, “Multigrid,” Academic Press, London, 2001.
|
[20]
|
J. W. Ruge and K. Stüben, “Algebraic Multigrid,” In: Multigrid Methods, Frontiers in Applied Mathematics, SIAM, Philadelphia, 1987, pp. 73-130.
doi:10.1137/1.9781611971057.ch4
|
[21]
|
W. Dahmen and L. Elsner, “Algebraic Multigrid Methods and the Schur Complement,” In: Kiel, Ed., Robust Multi-Grid Methods, Notes on Numerical Fluid Mechanics, Vol. 23, Vieweg, Braunschweig, 1989, pp. 58-68.
|
[22]
|
K. Stüben, “Algebraic Multigrid (AMG): An Introduction with Applications,” Technical Report 70, GMD, 1999.
|
[23]
|
I. Daubechies, “Orthonormal Bases of Compactly Supported Wavelets,” Communications on Pure and Applied Mathematics, Vol. 41, No. 7, 1988, pp. 909-996.
doi:10.1002/cpa.3160410705
|
[24]
|
I. Daubechies, “Ten Lectures on Wavelets,” CBMS-NSF Series in Applied Mathematics, Vol. 61, SIAM, Philadelphia, 1992.
|
[25]
|
A. Cohen, I. Daubechies and J.-C. Feauveau, “Biorthogonal Bases of Compactly Supported Wavelets,” Communications on Pure and Applied Mathematics, Vol. 45, No. 5, 1992, pp. 485-560. doi:10.1002/cpa.3160450502
|
[26]
|
D. K. Salkuyeh, “A New Approach to Compute Sparse Approximate Inverse Factors of a Matrix,” Applied Mathematics and Computation, Vol. 174, No. 2, 2006, pp. 1110-1121. doi:10.1016/j.amc.2005.06.011
|
[27]
|
L. Y. Kolotilina and A. Y. Yeremin, “Factorized Sparse Approximate Inverse Preconditioning I. Theory,” SIAM Journal on Matrix Analysis and Applications, Vol. 14, No. 1, 1993, pp. 45-58. doi:10.1137/0614004
|
[28]
|
L. Y. Kolotilina and A. Y. Yeremin, “Factorized Sparse Approximate Inverse Preconditioning II: Solution of 3D FE Systems on Massively Parallel Computers,” International Journal of High Speed Computing, Vol. 7, No. 2, 1995, pp. 191-215. doi:10.1142/S0129053395000117
|
[29]
|
E. Chow and Y. Saad, “Approximate Inverse Preconditioners via Sparse-Sparse Iterations,” SIAM Journal on Scientific Computing, Vol. 19, No. 3, 1998, pp. 995-1023.
doi:10.1137/S1064827594270415
|
[30]
|
I. Yavneh, C. H. Venner and A. Brandt, “Fast Multigrid Solution of the Advection Problem with Closed Characteristics,” SIAM Journal on Scientific Computing, Vol. 19, No. 1, 1998, pp. 111-125.
doi:10.1137/S1064827596302989
|
[31]
|
I. Yavneh, “Coarse-Grid Correction for Nonelliptic and Singular Perturbation Problems,” SIAM Journal on Scientific Computing, Vol. 19, No. 5, 1998, pp. 1682-1699.
doi:10.1137/S1064827596310998
|