Bibliography for Jacobi and Gauss-Seidel Iteration

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  1. Over-relaxation methods and coupled Markov chains for Monte Carlo simulation
    Barone, P.; Sebastiani, G.; Stander, J.
    Statistics and Computing, 2002, vol. 12, no. 1, pp. 17-26 , Ingenta.  
  2. 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.  
  3. On performance of SOR method for solving nonsymmetric linear systems
    Woznicki, Z. I.
    Journal of Computational and Applied Mathematics, 2001, vol. 137, no. ER1, pp. 145-176 , Ingenta.  
  4. 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.  
  5. Gauss-Seidel and Jacobi iterative methods for the solution of systems of linear equations.
    Defez Candel, Emilio
    Implementation with DERIVE. (Spanish) Epsilon 14 (1998), no. 1(40), 27--42, MathSciNet.  
  6. Basis of Eigenvectors and Principal Vectors Associated with Gauss-Seidel Matrix of A=Tridiag [-1 2 -1].
    Kohaupt, L.
    Siam review, 1998, vol. 40, no. 4, pp. 959 , Ingenta.  
  7. A generalization of the adaptive Gauss-Seidel method for Z-matrices.
    Kotakemori, Hisashi; Niki, Hiroshi; Okamoto, Naotaka
    Int. J. Comput. Math. 64 (1997), no. 3-4, 317--326, MathSciNet.  
  8. New simple criteria for the Jacobi, Gauss-Seidel and SOR iterations.
    Huang, T.-Z.
    Z. Angew. Math. Mech. 76 (1996), no. 1, 57--58, MathSciNet.  
  9. Acceleration of Five-Point Red-Black Gauss-Seidel in Multigrid for Poisson Equation.
    Zhang, Jun
    Applied mathematics and computation, 1996, vol. 80, no. 1, pp. 73 , Ingenta.  
  10. A Unified Proof for the Convergence of Jacobi and Gauss-Seidel Methods (in Classroom Notes)  
    Roberto Bagnara  
    SIAM Review, Vol. 37, No. 1. (Mar., 1995), pp. 93-97, Jstor.  
  11. Multigrid Smoothing Factors for Red-Black Gauss-Seidel Relaxation Applied to a Class of Elliptic Operators  
    Irad Yavneh  
    SIAM Journal on Numerical Analysis, Vol. 32, No. 4. (Aug., 1995), pp. 1126-1138, Jstor.  
  12. A parallel Gauss-Seidel method for block tridiagonal linear systems.
    Amodio, Pierluigi; Mazzia, Francesca
    SIAM J. Sci. Comput. 16 (1995), no. 6, 1451--1461, MathSciNet.  
  13. A Unified Proof for the Convergence of Jacobi and Gauss-Seidel Methods.
    Bagnara, Roberto
    Siam review, 1995, vol. 37, no. 1, pp. 93 , Ingenta.  
  14. 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.  
  15. Improving the SOR Method.
    Li, C.-J.; Evans, D.J.
    International journal of computer mathematics, 1994, vol. 54, no. 3/4, pp. 207 , Ingenta.  
  16. Sor-Secant Methods  
    Jose Mario Martinez  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 1. (Feb., 1994), pp. 217-226, Jstor.  
  17. Iterative Methods in Linear Algebra  
    Donald R. LaTorre   
    College Math Journal: Volume 24, Number 1, (1993),Pages: 79-88.   
  18. A modified Gauss-Seidel iteration for linear interval equations.
    Zhou, Ru-hai
    Numer. Math. J. Chinese Univ. (English Ser.) 2 (1993), no. 2, 225--233, MathSciNet.  
  19. 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.  
  20. Gauss-Seidel Method for Least-Distance Problems.
    Li, W.; Pardalos, P.M.; Han, C.G.
    Journal of optimization theory and applications, 1992, vol. 75, no. 3, pp. 487 , Ingenta.  
  21. Jacobi Iteration in Implicit Difference Schemes for the Wave Equation  
    D. B. Duncan, M. A. M. Lynch  
    SIAM Journal on Numerical Analysis, Vol. 28, No. 6. (Dec., 1991), pp. 1661-1679, Jstor.  
  22. Preconditioners for the Interval Gauss-Seidel Method  
    R. Baker Kearfott  
    SIAM Journal on Numerical Analysis, Vol. 27, No. 3. (Jun., 1990), pp. 804-822, Jstor.  
  23. Simulation of econometric models with the Gauss-Seidel method.
    Welfe, Aleksander; Zato'n, Wojciech
    Ekonom.-Mat. Obzor 26 (1990), no. 1, 9--26, MathSciNet.  
  24. 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.  
  25. 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.  
  26. 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.  
  27. Improving Jacobi and Gauss-Seidel iterations.
    Milaszewicz, J. P.
    Linear Algebra Appl. 93 (1987), 161--170, MathSciNet.  
  28. The Covergence Rate of a Multigrid Method with Gauss-Seidel Relaxation for the Poisson Equation  
    Dietrich Braess  
    Mathematics of Computation, Vol. 42, No. 166. (Apr., 1984), pp. 505-519, Jstor.  
  29. Convergence of Gauss-Seidel and related sequences.
    Speck, G. P.
    New Zealand Math. Mag. 14 (1977), no. 1, 37--41, MathSciNet.  
  30. The Convergence of Jacobi and Gauss-Seidel Iteration  
    Stewart Venit  
    Mathematics Magazine: Volume 48, Number 3, (1975), Pages: 163-167, MathSciNet.     
  31. 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.  
  32. An Extrapolated Gauss-Seidel Iteration for Hessenberg Matrices  
    L. J. Lardy  
    Mathematics of Computation, Vol. 27, No. 124. (Oct., 1973), pp. 921-926, Jstor.  
  33. Gauss-Seidel Convergence for Operators on Hilbert Space  
    John De Pillis  
    SIAM Journal on Numerical Analysis, Vol. 10, No. 1. (Mar., 1973), pp. 112-122, Jstor.  
  34. 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.  
  35. Generalized Overrelaxation and Gauss-Seidel Convergence on Hilbert Space  
    Michael P. Hanna  
    Proceedings of the American Mathematical Society, Vol. 35, No. 2. (Oct., 1972), pp. 524-530, Jstor.  
  36. Coupled Harmonic Equations, SOR, and Chebyshev Acceleration  
    L. W. Ehrlich  
    Mathematics of Computation, Vol. 26, No. 118. (Apr., 1972), pp. 335-343, Jstor.  
  37. Nonlinear Generalizations of Matrix Diagonal Dominance with Application to Gauss-Seidel Iterations  
    Jorge J. More  
    SIAM Journal on Numerical Analysis, Vol. 9, No. 2. (Jun., 1972), pp. 357-378, Jstor.  
  38. On Rates of Convergence of Jacobi and Gauss-Seidel Methods for M-Functions   
    T. A. Porsching  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 3. (Sep., 1971), pp. 575-582, Jstor.  
  39. Global Convergence of Newton-Gauss-Seidel Methods  
    Jorge J. More  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 325-336, Jstor.  
  40. 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.  
  41. Jacobi and Gauss-Seidel Methods for Nonlinear Network Problems  
    T. A. Porsching  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 3. (Sep., 1969), pp. 437-449, Jstor.  
  42. 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.  
  43. Monotone Iterations for Nonlinear Equations with Application to Gauss-Seidel Methods
    James M. Ortega, Werner C. Rheinboldt
    SIAM Journal on Numerical Analysis, Vol. 4, No. 2. (Jun., 1967), pp. 171-190, Jstor.  
  44. Nonlinear Difference Equations and Gauss-Seidel Type Iterative Methods  
    James M. Ortega, Maxine L. Rockoff  
    SIAM Journal on Numerical Analysis, Vol. 3, No. 3. (Sep., 1966), pp. 497-513, Jstor.  
  45. 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.  
  46. 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.  
  47. 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.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003