共查询到10条相似文献,搜索用时 0 毫秒
1.
Matthew M. Lin 《Linear and Multilinear Algebra》2018,66(7):1279-1298
This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a semigroup property depending only on the initial matrix pencil. Via this recursion relationship, we propose an accelerated iterative method to compute the stable subspace and use it to provide a theoretical result to solve the principal square root of a given matrix, both nonsingular and singular. We show that this method can not only find out the matrix square root, but also construct an iterative approach which converges to the square root with any desired order. 相似文献
2.
Zhao Yang 《Numerical Linear Algebra with Applications》2023,30(5):e2483
A class of negative matrices including Vandermonde-like matrices tends to be extremely ill-conditioned, and linear systems associated with this class of matrices appear in the polynomial interpolation problems. In this article, we present a fast and accurate algorithm with complexity to solve the linear systems whose coefficient matrices belong to the class of negative matrix. We show that the inverse of any such matrix is generated in a subtraction-free manner. Consequently, the solutions of linear systems associated with the class of negative matrix are accurately determined by parameterization matrices of coefficient matrices, and a pleasantly componentwise forward error is provided to illustrate that each component of the solution is computed to high accuracy. Numerical experiments are performed to confirm the claimed high accuracy. 相似文献
3.
H. Sadok 《Numerical Algorithms》1999,20(4):303-321
The Generalized Minimal Residual (GMRES) method and the Quasi-Minimal Residual (QMR) method are two Krylov methods for solving
linear systems. The main difference between these methods is the generation of the basis vectors for the Krylov subspace.
The GMRES method uses the Arnoldi process while QMR uses the Lanczos algorithm for constructing a basis of the Krylov subspace.
In this paper we give a new method similar to QMR but based on the Hessenberg process instead of the Lanczos process. We call
the new method the CMRH method. The CMRH method is less expensive and requires slightly less storage than GMRES. Numerical
experiments suggest that it has behaviour similar to GMRES.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
Summary.
Large, sparse nonsymmetric systems of linear equations with a
matrix whose eigenvalues lie in the right half plane may be solved by an
iterative method based on Chebyshev polynomials for an interval in the
complex plane. Knowledge of the convex hull of the spectrum of the
matrix is required in order to choose parameters upon which the
iteration depends. Adaptive Chebyshev algorithms, in which these
parameters are determined by using eigenvalue estimates computed by the
power method or modifications thereof, have been described by Manteuffel
[18]. This paper presents an adaptive Chebyshev iterative method, in
which eigenvalue estimates are computed from modified moments determined
during the iterations. The computation of eigenvalue estimates from
modified moments requires less computer storage than when eigenvalue
estimates are computed by a power method and yields faster convergence
for many problems.
Received May 13, 1992/Revised version received May 13,
1993 相似文献
5.
This article considers the robust regulation problem for a class of constrained linear switched systems with bounded additive disturbances. The proposed solution extends the existing robust tube based model predictive control (RTBMPC) strategy for non-switched linear systems to switched systems. RTBMPC utilizes nominal model predictions, together with tightened sets constraints, to obtain a control policy that guarantees robust stabilization of the dynamic systems in presence of bounded uncertainties. In this work, similar to RTBMPC for non-switched systems, a disturbance rejection proportional controller is used to ensure that the closed loop trajectories of the switched linear system are bounded in a tube centered on the nominal system trajectories. To account for the uncertainty related to all sub-systems, the gain of this controller is chosen to simultaneously stabilize all switching dynamics. The switched system RTBMPC requires an on-line solution of a Mixed Integer Program (MIP), which is computationally expensive. To reduce the complexity of the MIP, a sub-optimal design with respect to the previous formulation is also proposed that uses the notion of a pre-terminal set in addition to the usual terminal set to ensure stability. The RTBMPC design with the pre-terminal set aids in determining the trade-off between the complexity of the control algorithm with the performance of the closed-loop system while ensuring robust stability. Simulation examples, including a Three-tank benchmark case study, are presented to illustrate features of the proposed MPC. 相似文献
6.
M. Bertocchi 《Journal of Optimization Theory and Applications》1989,60(3):375-392
Numerical results are obtained on sequential and parallel versions of ABS algorithms for linear systems for both full matrices andq-band matrices. The results using the sequential algorithm on full matrices indicate the superiority of a particular implementation of the symmetric algorithm. The condensed form of the algorithm is well suited for implementation in a parallel environment, and results obtained on the IBM 4381 system favor a synchronous implementation over the asynchronous one. Results are obtained from sequential implementations of theLU, Cholesky, and symmetric algorithms of the ABS class forq-band matrices able to reduce memory storage. A simple parallelization of do-loops for calculating components gives interesting performances.This work has been developed in the framework of a collaboration between IBM-ECSEC, Rome, Italy, and the Department of Mathematics of the University of Bergamo, Bergamo, Italy.The author is grateful to Prof. J. Abaffy (University of Economics, Budapest), Prof. L. Dixon (Hatfield Polytechnic), and Prof. E. Spedicato (Department of Mathematics, University of Bergamo) for useful suggestions. 相似文献
7.
Despite its usefulness in solving eigenvalue problems and linear systems of equations, the nonsymmetric Lanczos method is known to suffer from a potential breakdown problem. Previous and recent approaches for handling the Lanczos exact and near-breakdowns include, for example, the look-ahead schemes by Parlett-Taylor-Liu [23], Freund-Gutknecht-Nachtigal [9], and Brezinski-Redivo Zaglia-Sadok [4]; the combined look-ahead and restart scheme by Joubert [18]; and the low-rank modified Lanczos scheme by Huckle [17]. In this paper, we present yet another scheme based on a modified Krylov subspace approach for the solution of nonsymmetric linear systems. When a breakdown occurs, our approach seeks a modified dual Krylov subspace, which is the sum of the original subspace and a new Krylov subspaceK
m
(w
j
,A
T
) wherew
j
is a newstart vector (this approach has been studied by Ye [26] for eigenvalue computations). Based on this strategy, we have developed a practical algorithm for linear systems called the MLAN/QM algorithm, which also incorporates the residual quasi-minimization as proposed in [12]. We present a few convergence bounds for the method as well as numerical results to show its effectiveness.Research supported by Natural Sciences and Engineering Research Council of Canada. 相似文献
8.
Summary.
An adaptive Richardson iteration method is described for the solution of
large sparse symmetric positive definite linear systems of equations with
multiple right-hand side vectors. This scheme ``learns' about the linear
system to be solved by computing inner products of residual matrices during
the iterations. These inner products are interpreted as block modified moments.
A block version of the modified Chebyshev algorithm is presented which yields
a block tridiagonal matrix from the block modified moments and the recursion
coefficients of the residual polynomials. The eigenvalues of this block
tridiagonal matrix define an interval, which determines the choice of relaxation
parameters for Richardson iteration. Only minor modifications are necessary
in order to obtain a scheme for the solution of symmetric indefinite linear
systems with multiple right-hand side vectors. We outline the changes required.
Received April 22, 1993 相似文献
9.
We prove that ?‐linear GMRES for solving a class of ?‐linear systems is faster than GMRES applied to the related ?‐linear systems in terms of matrix–vector products. Numerical examples are given to demonstrate the theoretical result. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
10.
Mátyás Barczy Mohamed Ben Alaya Ahmed Kebaier Gyula Pap 《Stochastic Processes and their Applications》2018,128(4):1135-1164
We consider a jump-type Cox–Ingersoll–Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases: subcritical, critical and supercritical. In the subcritical case we prove weak consistency and asymptotic normality, and, under an additional moment assumption, strong consistency as well. In the supercritical case, we prove strong consistency and mixed normal (but non-normal) asymptotic behavior, while in the critical case, weak consistency and non-standard asymptotic behavior are described. We specialize our results to so-called basic affine jump–diffusions as well. Concerning the asymptotic behavior of the MLE in the supercritical case, we derive a stochastic representation of the limiting mixed normal distribution, where the almost sure limit of an appropriately scaled jump-type supercritical CIR process comes into play. This is a new phenomenon, compared to the critical case, where a diffusion-type critical CIR process plays a role. 相似文献