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In the present paper, we propose block Krylov subspace methods for solving the Sylvester matrix equation AX–XB=C. We first consider the case when A is large and B is of small size. We use block Krylov subspace methods such as the block Arnoldi and the block Lanczos algorithms to compute approximations to the solution of the Sylvester matrix equation. When both matrices are large and the right-hand side matrix is of small rank, we will show how to extract low-rank approximations. We give some theoretical results such as perturbation results and bounds of the norm of the error. Numerical experiments will also be given to show the effectiveness of these block methods. 相似文献
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The truncated singular value decomposition (TSVD) is a popular solution method for small to moderately sized linear ill-posed
problems. The truncation index can be thought of as a regularization parameter; its value affects the quality of the computed
approximate solution. The choice of a suitable value of the truncation index generally is important, but can be difficult
without auxiliary information about the problem being solved. This paper describes how vector extrapolation methods can be
combined with TSVD, and illustrates that the determination of the proper value of the truncation index is less critical for
the combined extrapolation-TSVD method than for TSVD alone. The numerical performance of the combined method suggests a new
way to determine the truncation index.
In memory of Gene H. Golub. 相似文献
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K. Jbilou 《Linear algebra and its applications》2010,432(10):2473-1398
In the present paper, we propose preconditioned Krylov methods for solving large Lyapunov matrix equations AX+XAT+BBT=0. Such problems appear in control theory, model reduction, circuit simulation and others. Using the Alternating Direction Implicit (ADI) iteration method, we transform the original Lyapunov equation to an equivalent symmetric Stein equation depending on some ADI parameters. We then define the Smith and the low rank ADI preconditioners. To solve the obtained Stein matrix equation, we apply the global Arnoldi method and get low rank approximate solutions. We give some theoretical results and report numerical tests to show the effectiveness of the proposed approaches. 相似文献
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Numerical Algorithms - The bivariate sinc-Gauss sampling formula is introduced in Asharabi and Prestin (IMA J. Numer. Anal. 36:851–871, 2016) to approximate analytic functions of two... 相似文献
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In this paper, we introduce an extension of multiple set split variational inequality problem (Censor et al. Numer. Algor. 59, 301–323 2012) to multiple set split equilibrium problem (MSSEP) and propose two new parallel extragradient algorithms for solving MSSEP when the equilibrium bifunctions are Lipschitz-type continuous and pseudo-monotone with respect to their solution sets. By using extragradient method combining with cutting techniques, we obtain algorithms for these problems without using any product space. Under certain conditions on parameters, the iteration sequences generated by the proposed algorithms are proved to be weakly and strongly convergent to a solution of MSSEP. An application to multiple set split variational inequality problems and a numerical example and preliminary computational results are also provided. 相似文献
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In many problems of linear image restoration, the point spread function is assumed to be known even if this information is usually not available. In practice, both the blur matrix and the restored image should be performed from the observed noisy and blurred image. In this case, one talks about the blind image restoration. In this paper, we propose a method for blind image restoration by using convex constrained optimization techniques for solving large-scale ill-conditioned generalized Sylvester equations. The blur matrix is approximated by a Kronecker product of two matrices having Toeplitz and Hankel forms. The Kronecker product approximation is obtained from an estimation of the point spread function. Numerical examples are given to show the efficiency of our proposed method. 相似文献
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We propose and study the use of convex constrained optimization techniques for solving large-scale Generalized Sylvester Equations
(GSE). For that, we adapt recently developed globalized variants of the projected gradient method to a convex constrained
least-squares approach for solving GSE. We demonstrate the effectiveness of our approach on two different applications. First,
we apply it to solve the GSE that appears after applying left and right preconditioning schemes to the linear problems associated
with the discretization of some partial differential equations. Second, we apply the new approach, combined with a Tikhonov
regularization term, to restore some blurred and highly noisy images. 相似文献
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Bentbib A. H. Hachimi A. El Jbilou K. Ratnani A. 《Journal of Optimization Theory and Applications》2022,192(2):401-425
Journal of Optimization Theory and Applications - In the present paper, we propose two new methods for tensor completion of third-order tensors. The proposed methods consist in minimizing the... 相似文献