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On generalized successive overrelaxation methods for augmented linear systems. (English) Zbl 1083.65034
The authors present a generalized successive overrelaxation iterative algorithm for the augmented linear system corresponding to the Kuhn-Tucker conditions for quadratic programming or saddle point problems. They prove convergence and make a complete theoretical analysis for the optimal iteration parameters.

65F10Iterative methods for linear systems
65F50Sparse matrices (numerical linear algebra)
[1]Arrow, K., Hurwicz, L., Uzawa, H.: Studies in Nonlinear Programming. Stanford University Press, Stanford, 1958
[2]Axelsson, O.: Iterative Solution Methods. Cambridge University Press, Cambridge, 1994
[3]Bai, Z.-Z.: Parallel Iterative Methods for Large-Scale Systems of Algebraic Equations, Ph.D. Thesis, Department of Mathematics, Shanghai University of Science and Technology, Shanghai, March, 1993
[4]Bai, Z.-Z.: On the convergence of the generalized matrix multisplitting relaxed methods. Comm. Numer. Methods Engrg. 11, 363–371 (1995) · Zbl 0823.65027 · doi:10.1002/cnm.1640110410
[5]Bai, Z.-Z.: A class of modified block SSOR preconditioners for symmetric positive definite systems of linear equations. Adv. Comput. Math. 10, 169–186 (1999) · Zbl 0922.65033 · doi:10.1023/A:1018974514896
[6]Bai, Z.-Z.: Modified block SSOR preconditioners for symmetric positive definite linear systems. Ann. Oper. Res. 103, 263–282 (2001) · Zbl 1028.65018 · doi:10.1023/A:1012915424955
[7]Bai, Z.-Z., Golub, G.H., Pan, J.-Y.: Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems. Numer. Math. 98, 1–32 (2004) · Zbl 1056.65025 · doi:10.1007/s00211-004-0521-1
[8]Bai, Z.-Z., Li, G.-Q.: Restrictively preconditioned conjugate gradient methods for systems of linear equations. IMA J. Numer. Anal. 23, 561–580 (2003) · Zbl 1046.65018 · doi:10.1093/imanum/23.4.561
[9]Bai, Z.-Z., Wang, D.-R.: Generalized matrix multisplitting relaxation methods and their convergence. Numer. Math. J. Chinese Univ. (English Ser.) 2, 87–100 (1993)
[10]Bramble, J.H., Pasciak, J.E., Vassilev, A.T.: Analysis of the inexact Uzawa algorithm for saddle point problems. SIAM J. Numer. Anal. 34, 1072–1092 (1997) · Zbl 0873.65031 · doi:10.1137/S0036142994273343
[11]Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York and London, 1991
[12]Chan, R.H., Ng, M.K.: Conjugate gradient methods for Toeplitz systems. SIAM Rev. 38, 427–482 (1996) · Zbl 0863.65013 · doi:10.1137/S0036144594276474
[13]Elman, H.C., Golub, G.H.: Inexact and preconditioned Uzawa algorithms for saddle point problems. SIAM J. Numer. Anal. 31, 1645–1661 (1994) · Zbl 0815.65041 · doi:10.1137/0731085
[14]Fischer, B., Ramage, R., Silvester, D.J., Wathen, A.J.: Minimum residual methods for augmented systems. BIT 38, 527–543 (1998) · Zbl 0914.65026 · doi:10.1007/BF02510258
[15]Fortin, M., Glowinski, R.: Augmented Lagrangian Methods, Applications to the Numerical Solution of Boundary Value Problems. North-Holland, Amsterdam, 1983
[16]Golub, G.H., Van Loan, C.F.: Matrix Computations. 3rd Edition, The Johns Hopkins University Press, Baltimore and London, 1996
[17]Golub, G.H., Wu, X., Yuan, J.-Y.: SOR-like methods for augmented systems. BIT 41, 71–85 (2001) · Zbl 0991.65036 · doi:10.1023/A:1021965717530
[18]Henrici, P.: Applied and Computational Complex Analysis. Vol. 1: Power Series, Integration, Conformal Mapping and Location of Zeros, John Wiley & Sons, New York, London and Sydney, 1974
[19]Hestenes, M.R., Stiefel, E.L.: Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bureau Standards Section B 49, 409–436 (1952)
[20]Hu, J.-G.: Convergence of a generalized iterative matrix. Math. Numer. Sinica 6, 174–181 (1984) (In Chinese)
[21]Li, C.-J., Li, B.-J., Evans, D.J.: A generalized successive overrelaxation method for least squares problems. BIT 38, 347–356 (1998) · Zbl 0907.65043 · doi:10.1007/BF02512371
[22]Li, C.-J., Li, Z., Evans, D.J., Zhang, T.: A note on an SOR-like method for augmented systems. IMA J. Numer. Anal. 23, 581–592 (2003) · Zbl 1053.65020 · doi:10.1093/imanum/23.4.581
[23]Miller, J.J.H.: On the location of zeros of certain classes of polynomials with applications to numerical analysis. J. Inst. Math. Appl. 8, 397–406 (1971) · Zbl 0232.65070 · doi:10.1093/imamat/8.3.397
[24]Ng, M.K.: Preconditioning of elliptic problems by approximation in the transform domain. BIT 37, 885–900 (1997) · Zbl 0890.65042 · doi:10.1007/BF02510358
[25]Song, Y.-Z.: On the convergence of the generalized AOR method. Linear Algebra Appl. 256, 199–218 (1997) · Zbl 0872.65028 · doi:10.1016/S0024-3795(96)00028-6
[26]Song, Y.-Z.: On the convergence of the MAOR method. J. Comput. Appl. Math. 79, 299–317 (1997) · Zbl 0882.65017 · doi:10.1016/S0377-0427(97)00008-3
[27]Varga, R.S.: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs, N.J., 1962
[28]Wang, X.-M.: Generalized extrapolation principle and convergence of some generalized iterative methods. Linear Algebra Appl. 185, 235–272 (1993) · Zbl 0770.65019 · doi:10.1016/0024-3795(93)90215-A
[29]Wang, X.-M.: Convergence for a general form of the GAOR method and its application to the MSOR method. Linear Algebra Appl. 196, 105–123 (1994) · Zbl 0797.65028 · doi:10.1016/0024-3795(94)90318-2
[30]Young, D.M.: Iterative Solutions of Large Linear Systems. Academic Press, New York, 1971