Untitled

Golub, Gene H.; Vanderstraeten, Denis

doi:10.1023/a:1016637813615

Cited by 42 publications

(9 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…the spectrum of X −1 R lies into a disk of the complex plane having radius much smaller than the unity [6]. This last result, combined with relation (8), implicates that all the eigenvalues of the coefficient matrix X −1 Z of the preconditioned matrix system (4) will be clustered around the point (1, 0) of the complex plane, obtaining in this way the sought preconditioning effect [4] …”

Section: Discretized Efie and The Skew-hermitian Preconditioningmentioning

confidence: 79%

“…In order to obtain an effective preconditioning effect, P can be simple selected as follows [6]: let Z = X + R;…”

Section: Discretized Efie and The Skew-hermitian Preconditioningmentioning

confidence: 99%

“…the Hermitian and skew-Hermitian components of Z, respectively [6] (the apex H denotes the hermitian transpose of a matrix). On the basis of the above relation, the coefficient matrix of the preconditioned linear system defined by Eq.…”

Section: Discretized Efie and The Skew-hermitian Preconditioningmentioning

confidence: 99%

“…Now, if X dominates R in the sense of the norm · 2 , i.e. X 2 R 2 , the following relation on the spectral radius ρ of the product X −1 R is fulfilled [6,9] …”

Section: Discretized Efie and The Skew-hermitian Preconditioningmentioning

confidence: 99%

“…Nevertheless looking for specific strategies of preconditioning in relation to specific problems still seems to be the best way to reach the best results in terms of efficiency. In this study, we analyze the performances of a simple preconditioner based on the skew-hermitian component X of the impedance matrix Z [6]. The reminder of the work is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A simple preconditioner based on skew-Hermitian part of the discretized E-field Integral Equation

Angiulli¹,

Amendola

Arnieri

2013

IEICE Electron. Express

View full text Add to dashboard Cite

Abstract:It is well known that the rate of convergence of the Krylov Subspace Methods (KSMs) applied to the solution of the linear systems of equations arising from the discretization process of the E-Field Integral Equation (EFIE) by Method of Moments (MoM), can be improved by a suitable preconditioning strategy. In this paper, we analyze the performances of an easy preconditioner based on the skew-Hermitian part X of the impedance matrix Z. Numerical examples illustrate its performances and validate the proposed approach.

show abstract

Section: Discretized Efie and The Skew-hermitian Preconditioningmentioning

confidence: 79%

“…In order to obtain an effective preconditioning effect, P can be simple selected as follows [6]: let Z = X + R;…”

Section: Discretized Efie and The Skew-hermitian Preconditioningmentioning

confidence: 99%

Section: Discretized Efie and The Skew-hermitian Preconditioningmentioning

confidence: 99%

“…Now, if X dominates R in the sense of the norm · 2 , i.e. X 2 R 2 , the following relation on the spectral radius ρ of the product X −1 R is fulfilled [6,9] …”

Section: Discretized Efie and The Skew-hermitian Preconditioningmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A simple preconditioner based on skew-Hermitian part of the discretized E-field Integral Equation

Angiulli¹,

Amendola

Arnieri

2013

IEICE Electron. Express

View full text Add to dashboard Cite

show abstract

Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems

Krukier

Ren

2013

Numer. Linear Algebra Appl.

View full text Add to dashboard Cite

A generalized skew-Hermitian triangular splitting iteration method is presented for solving non-Hermitian linear systems with strong skew-Hermitian parts. We study the convergence of the generalized skew-Hermitian triangular splitting iteration methods for non-Hermitian positive definite linear systems, as well as spectrum distribution of the preconditioned matrix with respect to the preconditioner induced from the generalized skew-Hermitian triangular splitting. Then the generalized skew-Hermitian triangular splitting iteration method is applied to non-Hermitian positive semidefinite saddle-point linear systems, and we prove its convergence under suitable restrictions on the iteration parameters. By specially choosing the values of the iteration parameters, we obtain a few of the existing iteration methods in the literature. Numerical results show that the generalized skew-Hermitian triangular splitting iteration methods are effective for solving non-Hermitian saddle-point linear systems with strong skew-Hermitian parts.

show abstract

On SSOR‐like preconditioners for non‐Hermitian positive definite matrices

Bai

2015

Numerical Linear Algebra App

View full text Add to dashboard Cite

SUMMARY We construct, analyze, and implement SSOR‐like preconditioners for non‐Hermitian positive definite system of linear equations when its coefficient matrix possesses either a dominant Hermitian part or a dominant skew‐Hermitian part. We derive tight bounds for eigenvalues of the preconditioned matrices and obtain convergence rates of the corresponding SSOR‐like iteration methods as well as the corresponding preconditioned GMRES iteration methods. Numerical implementations show that Krylov subspace iteration methods such as GMRES, when accelerated by the SSOR‐like preconditioners, are efficient solvers for these classes of non‐Hermitian positive definite linear systems. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

Untitled

Cited by 42 publications

References 15 publications

A simple preconditioner based on skew-Hermitian part of the discretized E-field Integral Equation

A simple preconditioner based on skew-Hermitian part of the discretized E-field Integral Equation

Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems

On SSOR‐like preconditioners for non‐Hermitian positive definite matrices

Contact Info

Product

Resources

About