Frequency domain behavior of a set of parallel multigrid smoothing operators

References

• Banerjee R. N. Benson M. W. An Approximate Inverse Based Multigrid Approach to the Biharmonic Problem Lakehead University, Thunder Bay Ontario, Canada 1988 Mathematics Report No. 2-88
   Google Scholar
• Baumgardner , J. R. and Frederickson , P. O. 1985 . Icosahedral discretization of the two-sphere . SIAM J. Numer. Anal. , 22 : 1107 – 1115 .
   Web of Science ®Google Scholar
• Benson M. W. An Approximate Inverse Based Multigrid Approach to Thin Domain Elasticity Problems Lakehead University, Thunder Bay Ontario, Canada 1989 Mathematics Report No. 1-89
   Google Scholar
• Benson , M. W. and Frederickson , P. O. 1988 . “ Fast pseudo-inverse algorithms on hypercubes ” . In Multigrid Methods, Theory, Applications, and Supercomputing , Edited by: Mc Cormick , S. 23 – 33 . Marcel Dekker .
   Google Scholar
• Benson , M. W. and Frederickson , P. O. 1987 . “ Fast parallel algorithms for the Moore-Penrose pseudo-inverse ” . In Hypercube Multiprocessors , Edited by: Heath , M. T. 597 – 604 . SIAM .
   Google Scholar
• Benson , M. W. , Krettmann , J. and Wright , M. 1984 . Parallel algorithms for the solution of certain large sparse linear systems . Intern. J. Computer Math. , 16 : 245 – 260 .
   Web of Science ®Google Scholar
• Benson , M. W. and Frederickson , P. O. 1982 . Iterative solution of large sparse linear systems arising in certain multidimensional approximation problems . Utilitas Mathematica , 22 : 127 – 140 .
   Google Scholar
• Brandt , A. . Rigorous Local Mode Analysis of Multigrid, Preliminary Proceedings, Fourth Copper Mountain Conference on Multigrid Methods . Computational Mathematics Group . Denver : University of Colorado .
   Google Scholar
• Brandt , A. 1977 . Multi-level adaptive solution to boundary-value problems . Mathematics of Computation , 31 : 333 – 390 .
   Web of Science ®Google Scholar
• Frederickson P. O. Benson M. W. Fast Parallel Solution of Large Sparse Singular Systems Centre for Computer Science, Chr. Michelsen Institute Bergen, Norway 1986 Report CCS 86/9
   Google Scholar
• Frederickson P. O. Fast Approximate Inversion of Large Sparse Linear Systems Lakehead University, Thunder Bay Ontario, Canada 1975 Mathematics Report No. 7-75
   Google Scholar
• Mc Cormick , S. F. 1985 . Multigrid methods for variational problems: General theory for the V-cycle . SIAM J. Numer. Anal. , 22 : 634 – 643 .
   Web of Science ®Google Scholar
• Mc Cormick , S. F. and Ruge , J. W. 1982 . Multigrid methods for variational problems . SIAM J. Numer. Anal. , 19 : 924 – 929 .
   Web of Science ®Google Scholar
• Rabiner , L. R. and Gold , B. 1975 . Theory and Application of Digital Signal Processing , Prentice Hall .
   Google Scholar
• Stuben , K. and Trottenberg , U. 1982 . “ Multigrid methods: Fundamental algorithms, model problem analysis and applications ” . In Multigrid Methods, Springer-Verlag Lecture Notes in Mathematics 960 , Edited by: Hackbusch , W. and Trottenberg , U. 1 – 176 . Springer Verlag .
   Google Scholar
• Varga , R. S. 1962 . Matrix Iterative Analysis , Prentice Hall .
   Google Scholar