共查询到20条相似文献,搜索用时 15 毫秒
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Laurence Grammont 《Numerical Functional Analysis & Optimization》2013,34(7-8):729-754
The sensivtiity of the solution of the matrix Sylvester equation AX-XB=C is considered in the context of the classical perturbation theory. Our purpose is to find the most influent parameters in the sensitivity of the solution under perturbations in the data, and to compare the theoretical error bounds with numerical evidence. 相似文献
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Masoud Hajarian 《Mathematical Methods in the Applied Sciences》2014,37(13):2017-2028
It is well known that the least‐squares QR‐factorization (LSQR) algorithm is a powerful method for solving linear systems Ax = b and unconstrained least‐squares problem minx | | Ax ? b | | . In the paper, the LSQR approach is developed to obtain iterative algorithms for solving the generalized Sylvester‐transpose matrix equation the minimum Frobenius norm residual problem and the periodic Sylvester matrix equation Numerical results are given to illustrate the effect of the proposed algorithms. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Large-scale generalized Sylvester equations appear in several important applications. Although the involved operator is linear, solving them requires specialized techniques. Different numerical methods have been designed to solve them, including direct factorization methods suitable for small size problems, and Krylov-type iterative methods for large-scale problems. For these iterative schemes, preconditioning is always a difficult task that deserves to be addressed. We present and analyze an implicit preconditioning strategy specially designed for solving generalized Sylvester equations that uses a preconditioned residual direction at every iteration. The advantage is that the preconditioned direction is built implicitly, avoiding the explicit knowledge of the given matrices. Only the effect of the matrix-vector product with the given matrices is required. We present encouraging numerical experiments for a set of different problems coming from several applications. 相似文献
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Yifen Ke 《Journal of Applied Analysis & Computation》2020,10(3):972-985
A finite iterative algorithm is proposed to solve a class of complex generalized Sylvester tensor equations. The properties of this proposed algorithm are discussed based on a real inner product of two complex tensors and the finite convergence of this algorithm is obtained. Two numerical examples are offered to illustrate the effectiveness of the proposed algorithm. 相似文献
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Yufeng Xu Om P. Agrawal 《Communications in Nonlinear Science & Numerical Simulation》2013,18(12):3575-3589
This paper presents three generalizations of the van der Pol equation (VDPE) using newly proposed three new generalized K-, A- and B-operators. These operators allow kernel to be arbitrary. As a result, these operators provide a greater generalization of the VDPE than the fractional integral and differential operators do. Like the original VDPE, the generalized van der Pol equations (GVDPEs) are also nonlinear equations, and in most cases, they can not be solved analytically. Numerical algorithms are presented and used to solve the GVDPEs. Results for several examples are presented to demonstrate the effectiveness of the numerical algorithms, and to examine the behavior of the GVDPEs and the limit cycles associated with them. Although the numerical algorithms have been used to solve the GVDPEs only, they can also be used to solve many other generalized oscillators and generalized differential equations. This will be considered in the future. 相似文献
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An iterative method is proposed to solve generalized coupled Sylvester matrix equations, based on a matrix form of the least-squares QR-factorization (LSQR) algorithm. By this iterative method on the selection of special initial matrices, we can obtain the minimum Frobenius norm solutions or the minimum Frobenius norm least-squares solutions over some constrained matrices, such as symmetric, generalized bisymmetric and (R, S)-symmetric matrices. Meanwhile, the optimal approximate solutions to the given matrices can be derived by solving the corresponding new generalized coupled Sylvester matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the present method. 相似文献
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The purpose of this paper is to introduce a new system of generalized resolvent equations with corresponding system of variational
inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between system of generalized resolvent
equations and system of variational inclusions. The iterative algorithms for finding the approximate solutions of system of
generalized resolvent equations are proposed. The convergence of approximate solutions of system of generalized resolvent
equations obtained by the proposed iterative algorithm is also studied.
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Eugene Dulov Alexandre Sinitsyn 《Journal of Mathematical Analysis and Applications》2006,318(1):77-91
An analytical-numerical integration method for the generalized Liouville equation is proposed and analyzed. Taking into account a Cauchy condition f(q,p,t)|t=0=f0(q,p) for the phase space distribution function, we constructed the problem solution as series expansion in time variable t using orthogonal polynomials and Hermite function. Also we proved the corresponding convergence theorems under certain boundedness conditions upon a Liouville operator. 相似文献
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Peter Benner Ren-Cang Li Ninoslav Truhar 《Journal of Computational and Applied Mathematics》2009,233(4):1035-1045
This paper is concerned with the numerical solution of large scale Sylvester equations AX−XB=C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) [22] and Li and White (2002) [20] demonstrated that the so-called Cholesky factor ADI method with decent shift parameters can be very effective. In this paper we present a generalization of the Cholesky factor ADI method for Sylvester equations. An easily implementable extension of Penz’s shift strategy for the Lyapunov equation is presented for the current case. It is demonstrated that Galerkin projection via ADI subspaces often produces much more accurate solutions than ADI solutions. 相似文献
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Yuwen Luo 《Journal of Mathematical Analysis and Applications》2010,365(2):806-802
This paper studies the regularity of generalized magneto-hydrodynamics equation on the condition 0<α=β<3/2. It will show if ∇u∈Lp,q on [0,T) with
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研究了具有早期储备可修复系统,首先给出了该系统的预解式,对δ>0,γ=a+bi,固定a1,a2,满足-μ+δ相似文献
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Salahuddin 《Journal of Mathematical Analysis and Applications》2004,298(1):146-156
In this paper, we develop the sensitivity analysis for generalized set-valued variational inclusions and generalized resolvent equations. We establish the equivalence between the parametric generalized set-valued variational inclusions and parametric generalized resolvent equations, by using the resolvent operator technique without assuming the differentiability of the given data. 相似文献
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