Chronological inversion method for the dirac matrix in hybrid monte carlo

Nuclear Physics B

Volumn 484, Issue 1-2, 1997, Pages 353-374

  Brower, R C ^a   Ivanenko, T ^b   Levi, A R ^a   Orginos, K N ^c  

^a USA   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^c BROWN UNIVERSITY   (United States)

Author keywords

Conjugate gradient; Lattice QCD; Matrix inversion

Indexed keywords

EID: 0031579087     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(96)00579-2     Document Type: Article

References (24)

1. [1] R.D. Mawhinney, The status of the Teraflops projects, Nucl. Phys. (Proc. Supl) B 42 (1995) 140.
2. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
3. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
4. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
5. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
6. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
7. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
8. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
9. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
10. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
11. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
12. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
13. [2] G. Parisi and Y. Wu, Sci. Sin. 24 (1981) 483; J. Polonyi and H.W. Wyld, Phys. Rev. Lett. 51 (1983) 2257; S. Duane, Nucl. Phys. B 257 (1985) 652; G.C. Batroumi, G.R. Katz, A.S. Kronfeld, G.P. Lapage, B. Svetisky and K.G. Wilson, Phys. Rev. D 32 (1985) 2736; S. Duane and J. Kogut, Phys. Rev. Lett. 55 (1985) 2774; Nucl. Phys. B 275 (1986) 398; J. Callaway and A. Rhaman, Phys. Rev. D 34 (1986) 7911; S. Duane, A.D. Kennedy, B.J. Pendleton and D. Roweth, Phys. Lett B 195 (1987) 216; S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531; R. Gupta, G.W. Kilcup and S.R. Sharpe, Phys. Rev. D 38 (1988) 1278; R. Gupta et al., Phys. Rev. D 402072 (1989); D 44 (1991) 3272.
14. [3] "Those who cannot remember the past are condemned to repeat it", G. Santayana, The Life of Reason or Phases of Human Progress, New York, 1917.
15. [4] R.C. Brower, A.R. Levi and K. Orginos, Extrapolation methods for the Dirac inverter in hybrid Monte Carlo", talk presented at Lattice 94, Nucl. Phys. (Proc. Supl) B 42 (1995) 855.
16. [5] M. Lüscher, Nucl. Phys. B 418 (1994) 637.
17. [6] S. Gottlieb, W. Liu, D. Toussaint, R.L. Renken and R.L. Sugar, Phys Rev. D 35 (1987) 2531.
18. [7] R. Gupta, G. Kilcup and S. Sharpe, Phys Rev. D 38 (1988) 1278; R. Gupta, A. Patel, C. Baile, G. Guralnik, G. Kilcup and S. Sharpe, Phys Rev. D 40 (1989) 2072; R. Gupta, C. Baile, R Brickner, G. Kilcup, A. Patel and S. Sharpe, Phys Rev. D 44 (1991) 3272.
19. [7] R. Gupta, G. Kilcup and S. Sharpe, Phys Rev. D 38 (1988) 1278; R. Gupta, A. Patel, C. Baile, G. Guralnik, G. Kilcup and S. Sharpe, Phys Rev. D 40 (1989) 2072; R. Gupta, C. Baile, R Brickner, G. Kilcup, A. Patel and S. Sharpe, Phys Rev. D 44 (1991) 3272.
20. [7] R. Gupta, G. Kilcup and S. Sharpe, Phys Rev. D 38 (1988) 1278; R. Gupta, A. Patel, C. Baile, G. Guralnik, G. Kilcup and S. Sharpe, Phys Rev. D 40 (1989) 2072; R. Gupta, C. Baile, R Brickner, G. Kilcup, A. Patel and S. Sharpe, Phys Rev. D 44 (1991) 3272.
21. [8] A.H. Jazwinski, Stochastic processes and filtering theory (Academic Press, New York, 1970).
22. [9] C. Hill and J. Marshall, Applications of parallel Navier-Stokes solvers to ocean modelling, Proc. Parallel CDF 95 (Caltech) (1995).
23. [10] T. DeGrand and P. Rossi, Comp. Phys. Commun. 60 (1990) 211.
24. [11] G. Golub and C. Van Loan, Matrix Computations, 2nd Ed. (Johns Hopkins University Press, Baltimore, 1990).