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Year 2019, Volume: 9 Issue: 3, 549 - 553, 01.09.2019

Abstract

References

  • Zhang, H., Yin H., (2017), New proof of the gradient-based iterative algorithm for the Sylvester conjugate matrix equation, Computers and Mathematics with Applications, 74, pp. 3260-3270.
  • Ke, Y., Ma, C., (2017), The alternating direction methods for solving the Sylvester-type matrix equation AXB + CXTD = E, J. of Comput. Math., 35(5), pp. 620-641.
  • Larin, V.B., (2014), Algorithms for Solving a Unilateral Quadratic Matrix Equation and the Model Updating Problem, Int. Appl. Mech., 50 (3), pp. 321-334.
  • Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V., (1994), Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM.
  • Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M., (1995), LMI control toolbox users guide, The MathWorks Inc.
  • Aliev, F.A., Larin, V.B., (2017), A note about the solution of matrix Sylvestr equation, TWMS Journal of Pure and Applied Mathematics, 8(2), pp. 251-255.
  • Aliev, F.A., Larin, V.B., (2017), On the construction of general solution of the generalized Sylvester equation, TWMS J. App. Eng. Math., 7, pp. 1-6.
  • Aliev, F.A., Larin, V.B., Velieva, N.I., Gasimova, K.G., (2017), On periodic solution of generalize Sylvester matrix equation, Appl. Comput. Math., 16(1), pp. 78-84.
  • Pourgholi, R., Esfahan, A., Houlari, T., et al. (2017), An application of Sink-Galerkin method for solving the Tszou equation, Appl.Comput.Math., 16(3), pp. 240-256.
  • Aliev F.A., Larin V.B., On the solving of matrix equation of Sylvester type, Computational Methods For Differential Equations, 7(1), (2019), pp. 96-104.
  • Aliev F.A., Larin, V.B., (2009), About use of the Bass relations for solution of matrix equations, Appl. Comput. Math., 8(2), pp. 152-162.
  • Fikret A. Aliev, for a photograph and biography, see TWMS J. App. and Eng. Math., V.7, N.1, 2017, p.1.
  • Vladimir B. Larin, for a photograph and biography, see TWMS J. App. and Eng. Math., V.7, N.1, , p.1.

ON SOLUTION OF MODIFIED MATRIX SYLVESTER EQUATION

Year 2019, Volume: 9 Issue: 3, 549 - 553, 01.09.2019

Abstract

In the paper, the approach connected with the linear matrix inequalities for construction of solution of the modi ed Sylvester matrix equations, is used. The essence of the approach consists in replacement the initial equation with complex matrices, by two equations with real matrices. That allows to use for their solution the procedures of linear matrix inequalities. Eciency of o ered algorithm is shown on the examples.

References

  • Zhang, H., Yin H., (2017), New proof of the gradient-based iterative algorithm for the Sylvester conjugate matrix equation, Computers and Mathematics with Applications, 74, pp. 3260-3270.
  • Ke, Y., Ma, C., (2017), The alternating direction methods for solving the Sylvester-type matrix equation AXB + CXTD = E, J. of Comput. Math., 35(5), pp. 620-641.
  • Larin, V.B., (2014), Algorithms for Solving a Unilateral Quadratic Matrix Equation and the Model Updating Problem, Int. Appl. Mech., 50 (3), pp. 321-334.
  • Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V., (1994), Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM.
  • Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M., (1995), LMI control toolbox users guide, The MathWorks Inc.
  • Aliev, F.A., Larin, V.B., (2017), A note about the solution of matrix Sylvestr equation, TWMS Journal of Pure and Applied Mathematics, 8(2), pp. 251-255.
  • Aliev, F.A., Larin, V.B., (2017), On the construction of general solution of the generalized Sylvester equation, TWMS J. App. Eng. Math., 7, pp. 1-6.
  • Aliev, F.A., Larin, V.B., Velieva, N.I., Gasimova, K.G., (2017), On periodic solution of generalize Sylvester matrix equation, Appl. Comput. Math., 16(1), pp. 78-84.
  • Pourgholi, R., Esfahan, A., Houlari, T., et al. (2017), An application of Sink-Galerkin method for solving the Tszou equation, Appl.Comput.Math., 16(3), pp. 240-256.
  • Aliev F.A., Larin V.B., On the solving of matrix equation of Sylvester type, Computational Methods For Differential Equations, 7(1), (2019), pp. 96-104.
  • Aliev F.A., Larin, V.B., (2009), About use of the Bass relations for solution of matrix equations, Appl. Comput. Math., 8(2), pp. 152-162.
  • Fikret A. Aliev, for a photograph and biography, see TWMS J. App. and Eng. Math., V.7, N.1, 2017, p.1.
  • Vladimir B. Larin, for a photograph and biography, see TWMS J. App. and Eng. Math., V.7, N.1, , p.1.
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

F. A. Aliev This is me

V. B. Larin This is me

Publication Date September 1, 2019
Published in Issue Year 2019 Volume: 9 Issue: 3

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