Bibliography for Successive Over Relaxation

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  1. A note on an SOR-like method for augmented systems
    Li, C.; Li, Z.; Evans, D. J.; Zhang, T.
    IMA Journal of Numerical Analysis, 2003, vol. 23, no. 4, pp. 581-592, Ingenta.
  2. Newton-SOR Method for Fast Statistical Tomographic Image Reconstruction
    Kudo, H.; Sawada, S.
    Systems and Computers in Japan, 2003, vol. 34, no. 4, pp. 1-11, Ingenta.
  3. On the Optimal Relaxation Parameters to the Improved SOR Method with Orderings
    Muroya, Y.; Ishiwata, E.
    Tokyo Journal of Mathematics, 2002, vol. 25, no. 1, pp. 49-62, Ingenta.
  4. On performance of SOR method for solving nonsymmetric linear systems.   
    Wo'znicki, Zbigniew I.  
    J. Comput. Appl. Math. 137 (2001), no. 1, 145--176, MathSciNet.  
  5. Semiconvergence of block SOR method for singular linear systems with p-cyclic matrices.  
    Song, Yongzhong  
    J. Comput. Appl. Math. 130 (2001), no. 1-2, 217--229, MathSciNet.  
  6. Further Results on the Preconditioned SOR Method
    Martins, M. M.; Evans, D. J.; Yousif, W.
    International Journal of Computer Mathematics, 2001, vol. 77, no. 4, pp. 603-610, Ingenta.
  7. A new class of modified line-SOR algorithms
    Woznicki, Z.I.; Jedrzejec, H.A.
    Journal of Computational and Applied Mathematics, v 131, n 1-2, Jun 1, 2001, p 89-142, Compendex.
  8. A SOR-base Variable Preconditioned GCR Method
    Abe, K.; Zhang, S.-L.; Hasegawa, H.; Himeno, R.
    Transactions- Japan Society for Industrial and Applied Mathematics, 2001, vol. 11, no. 4, pp. 157-170, Ingenta.
  9. The Successive Over Relaxation Method (SOR) and Markov Chains
    Niethammer, W.
    Annals of Operations Research, 2001, vol. 103, no. 1/4, pp. 351-358, Ingenta.
  10. Can SOR be an efficient method for solving nonsymmetric linear systems?
    Woznicki, Z. I.
    Nonlinear Analysis Theory Methods and Applications, 2001, vol. 47, no. ER6, pp. 4295-4306, Ingenta.
  11. Successive overrelaxation (SOR) and related methods
    Hadjidimos, A.
    Journal of Computational and Applied Mathematics, v 123, n 1-2, Nov, 2000, p 177-199, Compendex.
  12. New parallel SOR method by domain partitioning.  
    Xie, Dexuan; Adams, Loyce  
    SIAM J. Sci. Comput. 20 (1999), no. 6, 2261--2281 (electronic), MathSciNet.  
  13. Note on the extended convergence of SOR for two-periodic Markov chains
    Niethammer, Wilhelm
    Linear Algebra and Its Applications, v 287, n 1-3, Jan 15, 1999, p 315-322 , Compendex.
  14. Improved SOR method with orderings and direct methods.  
    Ishiwata, Emiko; Muroya, Yoshiaki   
    Japan J. Indust. Appl. Math. 16 (1999), no. 2, 175--193, MathSciNet.  
  15. Adaptive Improved Block SOR Method with Orderings.
    Ishiwata, E.; Muroya, Y.; Isogai, K.
    Japan journal of industrial and applied mathematics, 1999, vol. 16, no. 3, pp. 443, Ingenta.
  16. A practical choice of parameters in improved SOR-Newton method with orderings.
    Ishiwata, E.
    Journal of Computational and Applied Mathematics, 1999, vol. 102, no. 2, pp. 315, Ingenta.
  17. Block SOR methods for rank-deficient least-squares problems.   
    Santos, C. H.; Silva, B. P. B.; Yuan, J. Y.   
    J. Comput. Appl. Math. 100 (1998), no. 1, 1--9, MathSciNet.  
  18. SOR as a preconditioner II
    DeLong, M.A.; Ortega, J.M.
    Applied Numerical Mathematics, v 26, n 4, Apr, 1998, p 465-481, Compendex.
  19. Preconditioning the linear system for the SOR method.   
    Li, Changjun; Evans, D. J.   
    Int. J. Comput. Math. 66 (1998), no. 1-2, 101--111, MathSciNet.  
  20. Main convergence theorems for the improved SOR method with orderings.   
    Ishiwata, Emiko; Muroya, Yoshiaki   
    Int. J. Comput. Math. 66 (1998), no. 1-2, 123--147, MathSciNet.  
  21. A Generalized SOR Method for Dense Linear Systems of Boundary Element Equations.
    Davey, K.; Bounds, S.
    SIAM journal on scientific computing, 1998, vol. 19, no. 3, pp. 953, Ingenta.
  22. Methodes iteratives de type SOR pour resoudre les problemes des moindres carres (SOR type iterative methods for solving least squares problems)
    Song, Yongzhong; Goro, Oumarou
    International Journal of Computer Mathematics, v 68, n 1-2, 1998, p 99-118 Language: French, Compendex.
  23. On SOR Waveform Relaxation Methods  
    Jan Janssen; Stefan Vandewalle
    SIAM Journal on Numerical Analysis, Vol. 34, No. 6. (Dec., 1997), pp. 2456-2481, Jstor.
  24. Stable spiral orbits of SOR Durand-Kerner's method applied ot the equation x to the d=0.
    Yamagishi, Y.
    Journal of computational and applied mathematics, 1997, vol. 82, no. 1/2, pp. 465, Ingenta.
  25. On nonlinear SOR-like methods, IV - SOR-secant method for nondifferentiable problems.
    Ishihara, K.; Yamamoto, T.
    Mathematica japonicae [sic], 1997, vol. 46, no. 1, pp. 103, Ingenta.
  26. Performance of the single-pass position monitor at SOR-RING
    Kudo, Hirofumi; Shinoe, Kenji; Takaki, Hiroyuki; Koseki, Tadashi; Nakamura, Norio; Kamiya, Yukihide; Honda, Tohru
    Proceedings of the IEEE Particle Accelerator Conference, v 2, 1997, p 2146-2148, Compendex.
  27. A note on the convergence of the Weierstrass sor method for polynomial roots.
    Petkovic, M.S.; Kjurkchiev, N.
    Journal of computational and applied mathematics, 1997, vol. 80, no. 1, pp. 163, Ingenta.
  28. On Nonlinear SOR-like Methods, II - Convergence of the SOR-Newton Method for Mildly Nonlinear Equations.
    Ishihara, K.; Muroya, Y.; Yamamoto, Tetsuro
    Japan journal of industrial and applied mathematics, 1997, vol. 14, no. 1, pp. 99, Ingenta.
  29. Implementation of the multicolored SOR method on a vector supercomputer
    Fujino, Seiji; Himeno, Ryutaro; Kojima, Akira; Terada, Kazuo
    IEICE Transactions on Information and Systems, v E80-D, n 4, Apr, 1997, p 518-523, Compendex.
  30. SOR as a parallel preconditioner
    DeLong, M.A.; Ortega, J.M. Source: Proc Conf Linear Nonlinear Conjugate Grad Rel Methods, 1996, p 143
    Database: , Compendex.
  31. The exact convergence and divergence domains of the SOR methods for 4-cyclic matrices.   
    Toutounian, Faezeh   
    J. Inst. Math. Comput. Sci. Math. Ser. 9 (1996), no. 3, 233--243, MathSciNet.  
  32. New simple criteria for the Jacobi, Gauss-Seidel, and SOR iterations
    Huang, T.-Z.
    Zeitschrift fuer Angewandte Mathematik und Mechanik, ZAMM, Applied Mathematics and Mechanics, v 76, n 1, 1996, p 57, Compendex.
  33. SOR as a preconditioner
    DeLong, M.A.; Ortega, J.M.
    Applied Numerical Mathematics, v 18, n 4, Oct, 1995, p 431, Compendex.
  34. Error checking of solving the Poisson's equation by SOR-step iteration method
    Tiau, Taixing
    Dianzi Keji Daxue Xuebao/Journal of University of Electronic Science and Technology of China, v 24, n 1, Feb, 1995, p 89, Compendex.
  35. Sor-Secant Methods  
    Jose Mario Martinez
    SIAM Journal on Numerical Analysis, Vol. 31, No. 1. (Feb., 1994), pp. 217-226, Jstor.
  36. The Sigma-Sor Algorithm and the Optimal Strategy for the Utilization of the Sor Iterative Method  
    Zbigniew I. Woznicki
    Mathematics of Computation, Vol. 62, No. 206. (Apr., 1994), pp. 619-644, Jstor.  
  37. Improving the SOR method
    Li, C.-J.; Evans, D.J.
    International Journal of Computer Mathematics, v 54, n 3-4, 1994, p 207, Compendex.
  38. On the convergence rate of SOR: a worst case estimate
    Oswald, P.
    Computing (Vienna/New York), v 52, n 3, 1994, p 245-255, Compendex.
  39. The Acceleration of the ADI Method by SOR.
    Li, C.; Evans, D. J.
    International journal of computer mathematics, 1994, vol. 50, no. 1/2, pp. 45, Ingenta.
  40. SOR iterative algorithm for the finite difference and the finite element methods that is efficient and parallelizable
    Wang, K.P.; Bruch, J.C. Jr.
    Advances in Engineering Software, v 21, n 1, 1994, p 37-48, Compendex.
  41. Convergence of the extrapolated AOR and SOR iterative methods
    Xinmin, Wang; Evans, D.J.
    International Journal of Computer Mathematics, v 52, n 1-2, 1994, p 65-74, Compendex.
  42. A successive over-relaxation method for quadratic programming problems with interval constraints.
    Shimazu, Yoshikazu; Fukushima, Masao; Ibaraki, Toshihide
    J. Oper. Res. Soc. Japan 36 (1993), no. 2, 73--89, MathSciNet.  
  43. Optimal stretched parameters for the SOR iterative method [CAM 1309].
    Noutsos, D.
    Journal of computational and applied mathematics, 1993, vol. 48, no. 3, pp. 293, Ingenta.
  44. A comparison of acceleration techniques applied to the SOR method.   
    da Cunha, Rudnei Dias; Hopkins, Tim
    Nonlinear numerical methods and rational approximation, II (Wilrijk, 1993), 247--260, Math. Appl., 296, Kluwer Acad. Publ., Dordrecht, 1994, MathSciNet.  
  45. On Domains of Superior Convergence of SSOR Method to that of the SOR Method.
    Hadijidimos, A.; Neumann, Michael
    Linear algebra and its applications, 1993, vol. 187, pp. 67, Ingenta.
  46. SOR method for multistaged separation columns computations.
    Onana, A.; Hikolo, A. Mbala
    Computers & chemical engineering, 1993, vol. 17, no. 8, pp. 799, Ingenta.
  47. Some sufficient conditions on the convergence of SOR iteration
    Dunhe, Gu
    Huadong Gongxueyuan Xuebao/Journal of East China Institute of Technology, n 2, 1993, p 23, Compendex.
  48. Is the Optimal Omega Best for the SOR Iteration Method?
    Eiermann, M.; Varga, R. S.
    Linear algebra and its applications, 1993, vol. 182, pp. 257, Ingenta.
  49. On domains of superior convergence of the SSOR method to that of the SOR method
    Hadjidimos, A.; Neumann, Michael
    Linear Algebra and Its Applications, v 187, Jul 1, 1993, p 67, Compendex.
  50. Convergence Analysis Without Regularity Assumptions for Multigrid Algorithms Based on SOR Smoothing  
    Junping Wang
    SIAM Journal on Numerical Analysis, Vol. 29, No. 4. (Aug., 1992), pp. 987-1001, Jstor.
  51. Optimum Modified SOR (MSOR) Method in a Special Case.
    Yeyios, A.K.
    Journal of computational mathematics, 1992, vol. 10, no. 4, pp. 358, Ingenta.
  52. A Newton-SOR Method for Spatial Price Equilibrium.
    Marcotte, Patrice; Marquis, Gerald; Zubieta, Lourdes
    Transportation science, 1992, vol. 26, no. 1, pp. 36, Ingenta.
  53. Diagonalizing the Adaptive SOR iteration Method.
    Dancis, Jerome
    SIAM journal on matrix analysis and applications, 1991, vol. 12, no. 4, pp. 661, Ingenta.
  54. On the efficiency of a SOR-like method suited to vector processors.
    Sugihara, M.; Oyanagi, Y.; Mori, M.
    Journal of computational and applied mathematics, 1991, vol. 35, pp. 33, Ingenta.
  55. On the efficiency of a SOR-line method suited to vector processors.
    Sugihara, M.; Oyanagi, Y.; Mori, M.
    Journal of computational and applied mathematics, 1991, vol. 35, no. 1/3, pp. 33, Ingenta.
  56. The Optimal omega Is Not Best for the SOR Iteration Method.
    Dancis, Jerome
    Linear algebra and its applications, 1991, vol. 154/156, pp. 819, Ingenta.
  57. A Parallelizable SOR-Like Method: Systems With Plus-Shaped and Linear Spectra.
    De Pillis, J
    Linear algebra and its applications, 1991, vol. 154/156, pp. 551, Ingenta.
  58. Block colouring schemes for the SOR method on local memory parallel computers.   
    Block, U.; Frommer, A.; Mayer, G.   
    Parallel Comput. 14 (1990), no. 1, 61--75, MathSciNet.  
  59. SOR Method and P-Cyclic Matrices (II).
    Evans, D.J.; Li, Changjun
    International journal of computer mathematics, 1990, vol. 37, no. 3/4, pp. 239, Ingenta.
  60. Nonlinear circuit analysis using the Newton-SOR continuation method.
    Cheng, K.K.M.; Everard, J.K.A.
    Electronics letters, 1990, vol. 26, no. 25, pp. 2120, Ingenta.
  61. Convergence Analysis of the Modified SOR (MSOR) Method.
    Yeyios, A.K.; Psimarni, A.
    International journal of computer mathematics, 1990, vol. 35, no. 1/4, pp. 231, Ingenta.
  62. Parallel-vector calculation of the SOR method
    Yokokawa, Mitsuo
    Trans. of the Japan Society of Mechanical Engineers, Part B, v 56, n 524, Apr, 1990, p 1062-1065, Compendex.
  63. SOR Method and P-Cyclic Matrices (I).
    Evans, D.J.; Li, C.
    International journal of computer mathematics, 1990, vol. 36, no. 1/2, pp. 57, Ingenta.
  64. Multicolour SOR method for the finite-element method
    Wu, C.H.
    Journal of Computational and Applied Mathematics, v 30, n 3, 1990, p 283, Compendex.
  65. Determination of the D^1/2 - Norm of the SOR Iterative Matrix for the Unsymmetric Case  
    D. J. Evans, C. Li
    Mathematics of Computation, Vol. 53, No. 187. (Jul., 1989), pp. 203-218, Jstor.  
  66. A Two-Level Four-Color SOR Method  
    C.-C. Jay Kuo; Bernard C. Levy
    SIAM Journal on Numerical Analysis, Vol. 26, No. 1. (Feb., 1989), pp. 129-151, Jstor.  
  67. The SOR Method on Parallel Computers.
    Niethammer, W.
    Numerische mathematik, 1989, vol. 56, no. 2/3, pp. 247--254, Ingenta.
  68. Optimum Extrapolated Method in a Special Case with Application to SOR Method.
    Psimarni, A.; Yeyios, A. K.
    International journal of computer mathematics, 1989, vol. 31, no. 1/2, pp. 95, Ingenta.
  69. Analysis of the SOR Iteration for the 9-Point Laplacian  
    Loyce M. Adams; Randall J. Leveque; David M. Young
    SIAM Journal on Numerical Analysis, Vol. 25, No. 5. (Oct., 1988), pp. 1156-1180, Jstor.  
  70. Toward an effective two-parameter SOR method.   
    Golub, Gene H.; de Pillis, John E.   
    Iterative methods for large linear systems (Austin, TX, 1988), 107--119, Academic Press, Boston, MA, 1990, MathSciNet.  
  71. Extrapolated Gauss-Seidel I and SOR methods for least-squares problems.   
    Evans, D. J.; Li, C.   
    Numer. Math. 53 (1988), no. 4, 485--498, MathSciNet.  
  72. Convergence des méthodes SOR à paramètre variable. (French) [On the convergence of variable parameter point SOR methods]   
    Khalil, Mohammed; Rigal, Alain   
    C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), no. 14, 629--634, MathSciNet.  
  73. A note on two block-SOR methods for sparse least squares problems.  
    Freund, R.  
    Linear Algebra Appl. 88/89 (1987), 211--221, MathSciNet.  
  74. Nonlinear successive over-relaxation.  
    Brewster, M. E.; Kannan, R.  
    Numer. Math. 44 (1984), no. 2, 309--315, MathSciNet.  
  75. On the convergence of the symmetric SOR method for matrices with red-black ordering.  
    Alefeld, G.  
    Numer. Math. 39 (1982), no. 1, 113--117, MathSciNet.  
  76. On a relaxed SOR-method applied to nonsymmetric linear systems.  
    Niethammer, W.; Schade, J.  
    J. Comput. Appl. Math. 1 (1975), no. 3, 133--136, MathSciNet.  
  77. SOR-Methods for the Eigenvalue Problem with Large Sparse Matrices  
    Axel Ruhe
    Mathematics of Computation, Vol. 28, No. 127. (Jul., 1974), pp. 695-710, Jstor.  
  78. Monotone Convergence of the Sor-Newton Iterative Technique  
    Charles W. Schelin
    SIAM Journal on Numerical Analysis, Vol. 10, No. 5. (Oct., 1973), pp. 933-938, Jstor.  
  79. Coupled Harmonic Equations, SOR, and Chebyshev Acceleration
    L. W. Ehrlich
    Mathematics of Computation, Vol. 26, No. 118. (Apr., 1972), pp. 335-343, Jstor.  
  80. On the Convergence of SOR Iterations for Finite Element Approximations to Elliptic Boundary Value Problems  
    George J. Fix; Kate Larsen  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 3. (Sep., 1971), pp. 536-547, Jstor.  
  81. Remarks on the Iterative Solution of the Neumann Problem on a Rectangle by Successive Line Over-Relaxation (in Technical Notes and Short Papers)  
    Fred W. Dorr  
    Mathematics of Computation, Vol. 23, No. 105. (Jan., 1969), pp. 177-179, Jstor.  
  82. Generalized consistent ordering and the optimum successive over-relaxation factor.  
    Nichols, Nancy K.; Fox, L.  
    Numer. Math. 13 1969 425--433, MathSciNet.  
  83. On generalizations of the theory of consistent orderings for successive over-relaxation methods.  
    Verner, J. H.; Bernal, M. J. M.  
    Numer. Math. 12 1968 215--222, MathSciNet.  
  84. A contribution to the successive over-relaxation method.  
    Humhal, Emil  
    Comment. Math. Univ. Carolinae 7 1966 237--247, MathSciNet.  
  85. A method for finding the optimum successive over-relaxation parameter.  
    Reid, J. K.  
    Comput. J. 9 1966 200--204, MathSciNet.  
  86. Estimation of the Successive Over-Relaxation Factor (in Technical Notes and Short Papers)  
    A. K. Rigler
    Mathematics of Computation, Vol. 19, No. 90. (Apr., 1965), pp. 302-307, Jstor.  
  87. Estimation of the successive over-relaxation factor.  
    Rigler, A. K.  
    Math. Comp. 19 1965 302--307, MathSciNet.  
  88. On Convergence Criteria for the Method of Successive Over-Relaxation (in Technical Notes and Short Papers)  
    C. G. Broyden  
    Mathematics of Computation, Vol. 18, No. 85. (Jan., 1964), pp. 136-141, Jstor.  
  89. On the Round-Off Error in the Method of Successive Over-Relaxation  
    M. Stuart Lynn
    Mathematics of Computation, Vol. 18, No. 85. (Jan., 1964), pp. 36-49, Jstor.  
  90. On the round-off error in the method of successive over-relaxation.  
    Lynn, M. Stuart
    Math. Comp. 18 1964 36--49, MathSciNet.  
  91. A practical technique for the determination of the optimum relaxation factor of the successive over-relaxation method.  
    Kulsrud, H. E.  
    Comm. ACM 4 1961 184--187, MathSciNet.  
  92. On Over and Under Relaxation in the Theory of the Cyclic Single Step Iteration
    A. Ostrowski
    Mathematical Tables and Other Aids to Computation, Vol. 7, No. 43. (Jul., 1953), pp. 152-159, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004