Eigenvalue Estimates for Preconditioned Saddle Point Matrices

Eigenvalue bounds for saddle point matrices on symmetric or, more generally, nonsymmetric form are derived and applied for preconditioned versions of the matrices. The preconditioners enable efficient iterative solution of the corresponding linear systems.

[1]  Rossitza S. Marinova,et al.  On a hybrid method of characteristics and central difference method for convection-diffusion problems , 1999 .

[2]  O. Axelsson A generalized conjugate gradient, least square method , 1987 .

[3]  Owe Axelsson,et al.  Preconditioning methods for linear systems arising in constrained optimization problems , 2003, Numer. Linear Algebra Appl..

[4]  Ulrich Langer,et al.  On the convergence factor of Uzawa's algorithm , 1986 .

[5]  Axel Klawonn,et al.  Block triangular preconditioners for nonsymmetric saddle point problems: field-of-values analysis , 1999, Numerische Mathematik.

[6]  O. Axelsson Preconditioning of Indefinite Problems by Regularization , 1979 .

[7]  Zhi-Hao Cao Fast uzawa algorithm for generalized saddle point problems , 2003 .

[8]  Ragnar Winther,et al.  A Preconditioned Iterative Method for Saddlepoint Problems , 1992, SIAM J. Matrix Anal. Appl..

[9]  R. Freund,et al.  Chebyshev polynomials are not always optimal , 1991 .

[10]  Ilse C. F. Ipsen A Note on Preconditioning Nonsymmetric Matrices , 2001, SIAM J. Sci. Comput..

[11]  Nicholas I. M. Gould,et al.  Constraint Preconditioning for Indefinite Linear Systems , 2000, SIAM J. Matrix Anal. Appl..

[12]  Axel Klawonn,et al.  Block-Triangular Preconditioners for Saddle Point Problems with a Penalty Term , 1998, SIAM J. Sci. Comput..

[13]  J. Pasciak,et al.  A preconditioning technique for indefinite systems resulting from mixed approximations of elliptic problems , 1988 .

[14]  Walter Zulehner,et al.  Analysis of iterative methods for saddle point problems: a unified approach , 2002, Math. Comput..

[15]  Owe Axelsson,et al.  Diagonally compensated reduction and related preconditioning methods , 1994, Numer. Linear Algebra Appl..

[16]  A. Wathen,et al.  Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners , 1994 .

[17]  Andrew J. Wathen,et al.  Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations , 2002, Numerische Mathematik.

[18]  Valeria Simoncini,et al.  Block triangular preconditioners for symmetric saddle-point problems , 2004 .

[19]  O. Axelsson Solving the Stokes problem on a massively parallel computer , 1999 .

[20]  Gene H. Golub,et al.  A Note on Preconditioning for Indefinite Linear Systems , 1999, SIAM J. Sci. Comput..