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The solutions of some operator equations

Dragana S. Cvetkovic-Ilic
대한수학회 (The Korean Mathematical Society)|2008.09|대한수학회지 (Journal of the KMS)|제45권 제5호|pp. 1417-1425

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참고문헌

키워드

Moore-Penrose inverseoperator equationg-invertibility
주제분류수학

초록

In this paper we consider the solvability and describe the set of the solutions of the operator equations AX + X*C = B and AXB + B*X*A*= C. This generalizes the results of D. S. Djordjevi´c [Explicit solution of the operator equation A*X+X*A=B, J. Comput. Appl. Math. 200 (2007), 701–704].

Abstract

In this paper we consider the solvability and describe the set of the solutions of the operator equations AX + X*C = B and AXB + B*X*A*= C. This generalizes the results of D. S. Djordjevi´c [Explicit solution of the operator equation A*X+X*A=B, J. Comput. Appl. Math. 200 (2007), 701–704].

참고문헌 (10)

  1. Ouvrages de Mathematiques de la SMC, "Generalized Inverses, Theory and applications. Second edition. CMS Books in Mathematics", pp.2003, A. Ben-Israel
  2. S. L. Campbell, "Generalized Inverses of Linear Transformations, Corrected reprint of the 1979 original" (1991), Dover Publications, Inc.
  3. S. R. Caradus, "Generalized Inverses and Operator Theory, Queen’s Papers in Pure and Applied Mathematics", pp.50~ (1978), Queen’s University
  4. D. S. Djordjevi´c, "Explicit solution of the operator equation A∗X+X∗A = B", Journal of Computational and Applied Mathematics, 200(2), pp.701~704 (2007)
  5. R. E. Harte, "Invertibility and singularity for bounded linear operators, Monographs and Textbooks in Pure and Applied Mathematics", pp.109~ (1988), Marcel Dekker, Inc.
  6. P. Kirrinnis, "Fast algorithms for the Sylvester equation AX − XB⊤ = C", Theoretical Computer Science, 259(1), pp.623~638 (2001)
  7. G. Kitagawa, "An algorithm for solving the matrix equation X = FXFT + S", International Journal of Control, 25(5), pp.745~753 (1977)
  8. Y. X. Peng, "An iteration method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C", Applied Mathematics and Computation, 160(3), pp.763~777 (2005)
  9. Z. Y. Peng, "The reflexive and anti-reflexive solutions of the matrix equation AX = B", Linear Algebra and its Applications, 375, pp.147~155 (2003)
  10. D. C. Sorensen, "The Sylvester equation and approximate balanced reduction", Linear Algebra and its Applications, 351, pp.671~700 (2002)

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