A New Iterative Scheme for Solving the Semi Sylvester Equation

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References

[1] R. Bhatia and P. Rosenthal, “How and Why to Solve the Operator Equation AX - XB = Y,” Bulletin London Mathematical Society, Vol. 29, No. 1, 1997, pp. 1-21.
doi:10.1112/S0024609396001828

[2] G. H. Golub and C. F. Van Loan, “Matrix Computations,” 3rd Edition, Johns Hopkins University Press, Baltimore, 1996.

[3] V. Sima, “Algorithms for Linear-Quadratic Optimization,” Vol. 200, Pure and Applied Mathematics, Marcel Dekker, Inc., New York, 1996.

[4] B. Datta, “Numerical Methods for Linear Control Systems,” Elsevier Academic Press, New York, 2004.

[5] A. Lu and E. Wachspress, “Solution of Lyapunov Equations by ADI Iteration,” Computers & Mathematics with Applications, Vol. 21, 1991, pp. 43-58.
doi:10.1016/0898-1221(91)90124-M

[6] A. C. Antoulas, “Approximation of Large-Scale Dynamical Systems,” Advances in Design and Control, SIAM, Philadelphia, 2005.

[7] U. Baur and P. Benner, “Cross-Gramian Based Model Reduction for Data-Sparse Systems,” Technical Report, Fakultat fur Mathematik, TU Chemnitz, Chemnitz, 2007.

[8] D. Sorensen and A. Antoulas, “The Sylvester Equation and Approximate Balanced Reduction,” Linear Algebra and Its Applications, Vol. 351-352, 2002, pp. 671-700.
doi:10.1016/S0024-3795(02)00283-5

[9] G. H. Golub, S. Nash and C. Van Loan, “A Hessenberg Schur Method for the Problem AX + XB = C,” IEEE Transactions on Automatic Control, Vol. 24, No. 6, 1979, pp. 909-913. doi:10.1109/TAC.1979.1102170

[10] P. Benner, “Factorized Solution of Sylvester Equations with Applications in Control,” In: B. De Moor, B. Motmans, J. Willems, P. Van Dooren and V. Blondel, Eds., Proceedings of the 16th International Symposium on Mathematical Theory of Network and Systems, Leuven, 5-9 July 2004.

[11] W. D. Hoskins, D. S. Meek and D. J. Walton, “The Numerical Solution of the Matrix Equation XA + AY = F,” BIT, Vol. 17, 1977, pp. 184-190.

[12] D. Y. Hu and L. Reichel, “Application of ADI Iterative Methods to the Restoration of Noisy Images,” Linear Algebra and Its Applications, Vol. 172, No. 15, 1992, pp. 283-313. doi:10.1016/0024-3795(92)90031-5

[13] A. El Guennouni, K. Jbilou and A. J. Riquet, “Block Krylov Subspace Methods for Solving Large Sylvester Equations,” Numerical Algorithms, Vol. 29, No. 1, 2002, pp. 75-96. doi:10.1023/A:1014807923223

[14] K. Jbilou, “Low Rank Approximate Solutions to Large Sylvester Matrix Equations,” Applied Mathematics and Computation, Vol. 177, No. 1, 2006, pp. 365-376.
doi:10.1016/j.amc.2005.11.014

[15] M. Robb and M. Sadkane, “Use of Near-Breakdowns in the Block Arnoldi Method for Solving Large Sylvester Equations,” Applied Numerical Mathematics, Vol. 58, No. 4, 2008, pp. 486-498. doi:10.1016/j.apnum.2007.01.025

[16] G. H. Golub, S. Nash and C. Van Loan, “A Hessenberg Schur Method for the Problem AX + XB = C,” IEEE Transactions on Automatic Control, No. 24, No. 6, 1979, pp. 909-913.

[17] T. Chan and M. Ng, “Galerkin Projection Methods for Solving Multiple Linear Systems,” Department of Mathematics, University of California, Los Angeles, 1996.

[18] S. Karimi, “A New Iterative Solution Method for Solving Multiple Linear Systeams,” Advances in Linear Algebra and Matrix Theory, Vol. 1, 2012, pp. 25-30.
doi:10.4236/alamt.2012.23004