A note on spectrum analysis of augmentation block preconditioned generalized saddle point matrices
نویسندگان
چکیده
منابع مشابه
On the eigenvalues and eigenvectors of nonsymmetric saddle point matrices preconditioned by block triangular matrices
Block lower triangular and block upper triangular matrices are popular preconditioners for nonsymmetric saddle point matrices. In this note we show that a block lower triangular preconditioner gives the same spectrum as a block upper triangular preconditioner and that the eigenvectors of the two preconditioned systems are related. Nonsingular saddle point matrices of the form
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New eigenvalue bounds for symmetric matrices of saddle point form are derived and applied for preconditioned versions of the matrices. The preconditioners enable efficient iterative solution of the corresponding linear systems with, for some important applications, an optimal order of computational complexity.
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where A is symmetric positive definite (SPD), C is symmetric semi-positive definite, and B is of full rank. System of the form (1) arises in a variety of scientific and engineering applications, such as constrained optimization, least squares. We refer the reader to [1] for a more detailed list of applications and numerical solution techniques of (1). Recently, drawing on previous works: [2, 3]...
متن کاملOn eigenvalue distribution of constraint-preconditioned symmetric saddle point matrices
This paper is devoted to the analysis of the eigenvalue distribution of two classes of block preconditioners for the generalized saddle point problem. Most of the bounds developed improve those appeared in previously published works. Numerical results onto a realistic test problem give evidence of the effectiveness of the estimates on the spectrum of preconditioned matrices. Copyright © 2011 Jo...
متن کاملSparse block factorization of saddle point matrices
The factorization method presented in this paper takes advantage of the special structures and properties of saddle point matrices. A variant of Gaussian elimination equivalent to the Cholesky’s factorization is suggested and implemented for factorizing the saddle point matrices block-wise with small blocks of order 1 and 2. The Gaussian elimination applied to these small blocks on block level ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2013
ISSN: 0377-0427
DOI: 10.1016/j.cam.2012.08.024