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Eigenvalue Bounds (eigenvalue + bound)

Distribution by Scientific Domains
Mathematics and Statistics57%
Engineering42%

Selected Abstracts

Eigenvalue bounds for some classes of P -matrices

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 11-12 2009
J. M. PeñaArticle first published online: 28 JUL 200
Abstract Eigenvalue bounds are provided. It is proved that the minimal eigenvalue of a Z -matrix strictly diagonally dominant with positive diagonals lies between the minimal and the maximal row sums. A similar upper bound does not hold for the minimal eigenvalue of a matrix strictly diagonally dominant with positive diagonals but with off-diagonal entries with arbitrary sign. Other new bounds for nonsingular M -matrices and totally nonnegative matrices are obtained. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Computing eigenvalue bounds of structures with uncertain-but-non-random parameters by a method based on perturbation theory

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2007
Huinan Leng
Abstract In this paper, an eigenvalue problem that involves uncertain-but-non-random parameters is discussed. A new method is developed to evaluate the reliable upper and lower bounds on frequencies of structures for these problems. In this method the matrix in the deviation amplitude interval is considered to be a perturbation around the nominal value of the interval matrix, and the upper and lower bounds to the maximum and minimum eigenvalues of this perturbation matrix are computed, respectively. Then based on the matrix perturbation theory, the eigenvalue bounds of the original interval eigenvalue problem can be obtained. Finally, two numerical examples are provided and the results show that the proposed method is reliable and efficient. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Computing bounds to real eigenvalues of real-interval matrices

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2008
Huinan Leng
Abstract In this study, a new method with algorithms for computing bounds to real eigenvalues of real-interval matrices is developed. The algorithms are based on the properties of continuous functions. The method can provide the tightest eigenvalue bounds and improve some former research results. Numerical examples illustrate the applicability and effectiveness of the new method. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Eigenvalue estimates for preconditioned saddle point matrices

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 4 2006
Owe Axelsson
Abstract New accurate eigenvalue bounds for symmetric matrices of saddle point form are derived and applied for both unpreconditioned and preconditioned versions of the matrices. The estimates enable a better understanding of how preconditioners should be chosen. The preconditioners provide efficient iterative solution of the corresponding linear systems with, for some important applications, an optimal order of computational complexity. The methods are applied for Stokes problem and for linear elasticity problems. Copyright © 2005 John Wiley & Sons, Ltd. [source]

A preconditioner for generalized saddle point problems: Application to 3D stationary Navier-Stokes equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2006
C. Calgaro
Abstract In this article we consider the stationary Navier-Stokes system discretized by finite element methods which do not satisfy the inf-sup condition. These discretizations typically take the form of a variational problem with stabilization terms. Such a problem may be transformed by iteration methods into a sequence of linear, Oseen-type variational problems. On the algebraic level, these problems belong to a certain class of linear systems with nonsymmetric system matrices ("generalized saddle point problems"). We show that if the underlying finite element spaces satisfy a generalized inf-sup condition, these problems have a unique solution. Moreover, we introduce a block triangular preconditioner and we show how the eigenvalue bounds of the preconditioned system matrix depend on the coercivity constant and continuity bounds of the bilinear forms arising in the variational problem. Finally we prove that the stabilized P1-P1 finite element method proposed by Rebollo is covered by our theory and we show that the condition number of the preconditioned system matrix is independent of the mesh size. Numerical tests with 3D stationary Navier-Stokes flows confirm our results. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006 [source]