In this article, we propose an iterative algorithm to compute the minimum norm least-squares solution of AXB + CYD = E, based on a matrix form of the algorithm LSQR for solving the least squares problem. We then apply...
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In this article, we propose an iterative algorithm to compute the minimum norm least-squares solution of AXB + CYD = E, based on a matrix form of the algorithm LSQR for solving the least squares problem. We then apply this algorithm to compute the minimum norm least-squares centrosymmetric solution of min(X) parallel to AXB - E parallel to(F). Numerical results are provided to verify the efficiency of the proposed method.
This paper deals with developing a robust iterative algorithm to find the least-squares (P, Q)-orthogonal symmetric and skew-symmetric solution sets of the generalized coupled matrix equations. To this end, first, som...
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This paper deals with developing a robust iterative algorithm to find the least-squares (P, Q)-orthogonal symmetric and skew-symmetric solution sets of the generalized coupled matrix equations. To this end, first, some properties of these type of matrices are established. Furthermore, an approach is offered to determine the optimal approximate (P, Q)-orthogonal (skew-)symmetric solution pair corresponding to a given arbitrary matrix pair. Some numerical experiments are reported to confirm the validity of the theoretical results and to illustrate the effectiveness of the proposed algorithm.
In this paper, we focus on the following coupled linear matrix equations M-i(X, Y) = M-i1(X) + M-i2(Y) = Li, with M-il(W) = (q)Sigma(j= 1) ( t(1)((l))Sigma(lambda=1) A(ij lambda)((l)) W-j B-ij lambda((l)) +t(2)((l))Si...
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In this paper, we focus on the following coupled linear matrix equations M-i(X, Y) = M-i1(X) + M-i2(Y) = Li, with M-il(W) = (q)Sigma(j= 1) ( t(1)((l))Sigma(lambda=1) A(ij lambda)((l)) W-j B-ij lambda((l)) +t(2)((l))Sigma(mu=1) C-ij lambda((l)) W-j D-ij lambda((l)) + t(3)((l))Sigma(lambda=1) E-ij lambda((l)) W-j B-j(T) F-ij lambda((l)) ) l=1,2 where A(ij lambda)((l)) B-ij lambda((l)) C-ij lambda j((l)) D-ij lambda((l)) E-ij lambda((l)) F-ij lambda((l)) and Li (for i is an element of I [1, p]) are given matrices with appropriate dimensions defined over complex number field. Our object is to obtain the solution groups X = (X-1, X-2,..., X-q) and Y = (Y-1, Y-2,..., Y-q) of the considered coupled linear matrix equations such that X and Y are the groups of the Hermitian reflexive and skew-Hermitian matrices, respectively. To do so, an iterative algorithm is proposed which stops within finite number of steps in the exact arithmetic. Moreover, the algorithm determines the solvability of the mentioned coupled linear matrix equations over the Hermitian reflexive and skew-Hermitian matrices, automatically. In the case that the coupled linear matrix equations are consistent, the least-norm Hermitian reflexive and skew-Hermitian solution groups can be computed by choosing suitable initial iterative matrix groups. In addition, the unique optimal approximate Hermitian reflexive and skew-Hermitian solution groups to given arbitrary matrix groups are derived. Finally, some numerical experiments are reported to illustrate the validity of our established theoretical results and feasibly of the presented algorithm.
The present work proposes a finite iterative algorithm to find the least squares solutions of periodic matrix equations over symmetric -periodic matrices. By this algorithm, for any initial symmetric -periodic matrice...
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The present work proposes a finite iterative algorithm to find the least squares solutions of periodic matrix equations over symmetric -periodic matrices. By this algorithm, for any initial symmetric -periodic matrices, the solution group can be obtained in finite iterative steps in the absence of round-off errors, and the solution group with least Frobenius norm can be obtained by choosing a special kind of initial matrices. Furthermore, in the solution set of the above problem, the unique optimal approximation solution group to a given matrix group in the Frobenius norm can be derived by finding the least Frobenius norm symmetric -periodic solution of a new corresponding minimum Frobenius norm problem. Finally, numerical examples are provided to illustrate the efficiency of the proposed algorithm and testify the conclusions suggested in this paper.
In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=*** expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitiv...
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In this study,an iterative algorithm is proposed to solve the nonlinear matrix equation X+A∗eXA=*** expressions for mixed and componentwise condition numbers with their upper bounds are derived to measure the sensitivity of the considered nonlinear matrix *** analysis for the derived condition numbers and the proposed algorithm are *** proposed iterative algorithm reduces the number of iterations significantly when incorporated with exact line *** condition number seems more reliable to detect the sensitivity of the considered equation than mixed condition number as validated by numerical examples.
In this paper, we develop a new iterative algorithm for solving a class of nonlinear mixed implicit variational inequalities and give the convergence analysis of the iterative sequences generated by the algorithms. In...
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In this paper, we develop a new iterative algorithm for solving a class of nonlinear mixed implicit variational inequalities and give the convergence analysis of the iterative sequences generated by the algorithms. In our results, we do not assume that the mapping is strongly monotone, nor do we assume that the mapping is surjective. (C) 2003 Elsevier Science Ltd. All rights reserved.
A useful technique for discrete-time system modeling and control consists of block-diagonalizing the system state matrix. The present paper proposes a new iterative algorithm for accomplishing this objective, and make...
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A useful technique for discrete-time system modeling and control consists of block-diagonalizing the system state matrix. The present paper proposes a new iterative algorithm for accomplishing this objective, and makes a comparison with other algorithms available in the literature.
Acoustic microscopy is capable of providing high-resolution images of small objects. When such a microscope operates in the transmission mode, it produces simply a shadowgraph of all the structures encountered by the ...
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Acoustic microscopy is capable of providing high-resolution images of small objects. When such a microscope operates in the transmission mode, it produces simply a shadowgraph of all the structures encountered by the acoustic wave passing through the object. The resultant images are difficult to comprehend because of diffraction and overlapping of complex structures. Scanning tomographic acoustic microscopy (STAM) overcomes these difficulties and produces unambiguous micrographs of objects of substantial thickness and complexity. STAM uses the back-and-forth propagation algorithm to reconstruct tomograms of various layers to be imaged. When these layers are physically close to one another, ambiguities appear in the reconstructed images. Using an iterative algorithm eliminates these ambiguities and resolves layers that are only two wavelengths apart.
A new iterative algorithm is suggested for calculating spectral parameters of a quadratic bunch of partially symmetrical compact operators in the Hilbert space.
A new iterative algorithm is suggested for calculating spectral parameters of a quadratic bunch of partially symmetrical compact operators in the Hilbert space.
In this paper, the auxiliary principle technique is extended to study a system of generalized set-valued strongly nonlinear mixed implicit quasi-variational-like inequalities problem in Hilbert spaces. First, we estab...
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In this paper, the auxiliary principle technique is extended to study a system of generalized set-valued strongly nonlinear mixed implicit quasi-variational-like inequalities problem in Hilbert spaces. First, we establish the existence of solutions of the corresponding system of auxiliary variational inequalities problem. Then, using the existence result, we construct a new iterative algorithm. Finally, both the existence of solutions of the original problem and the convergence of iterative sequences generated by the algorithm are proved. We give an affirmative answer to the open problem raised by Noor et al. (Korean J. Comput. Appl. Math. 1:73-89, 1998;J. Comput. Appl. Math. 47:285-312, 1993). Our results improve and extend some known results.
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