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]  Owe Axelsson,et al.  On a robust and scalable linear elasticity solver based on a saddle point formulation , 1999 .

[2]  Axel Klawonn,et al.  An Optimal Preconditioner for a Class of Saddle Point Problems with a Penalty Term , 1995, SIAM J. Sci. Comput..

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

[4]  V. Simoncini,et al.  Block--diagonal and indefinite symmetric preconditioners for mixed finite element formulations , 1999 .

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

[6]  Igor E. Kaporin,et al.  High quality preconditioning of a general symmetric positive definite matrix based on its U , 1998 .

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

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

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

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

[11]  Gene H. Golub,et al.  A Preconditioner for Generalized Saddle Point Problems , 2004, SIAM J. Matrix Anal. Appl..

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

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

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

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

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

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

[18]  Ilaria Perugia,et al.  Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations , 2000, Numer. Linear Algebra Appl..

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

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

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

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

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

[24]  Michele Benzi,et al.  Spectral Properties of the Hermitian and Skew-Hermitian Splitting Preconditioner for Saddle Point Problems , 2005, SIAM J. Matrix Anal. Appl..

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

[26]  Gene H. Golub,et al.  Numerical solution of saddle point problems , 2005, Acta Numerica.

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