Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



First order difference system-
existence and uniqueness

Authors: K. N. Murty, P. V. S. Anand and V. Lakshmi Prasannam
Journal: Proc. Amer. Math. Soc. 125 (1997), 3533-3539
MSC (1991): Primary 39A10, 34B05
MathSciNet review: 1443846
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, the general solution of the homogeneous matrix difference system is constructed in terms of two fundamental matrix solutions. The general solution of the inhomogeneous matrix difference system is established by the variation of parameters formula. A unique solution of the two-point boundary value problem associated with the matrix difference system is constructed by applying the QR-algorithm and the Bartels-Stewart algorithm.

References [Enhancements On Off] (What's this?)

  • 1. Ravi P. Agarwal, On multipoint boundary value problems for discrete equations, J. Math. Anal. Appl. 96 (1983), no. 2, 520–534. MR 719333, 10.1016/0022-247X(83)90058-6
  • 2. V. Lakshmikantham and D. Trigiante, Theory of difference equations, Mathematics in Science and Engineering, vol. 181, Academic Press, Inc., Boston, MA, 1988. Numerical methods and applications. MR 939611
  • 3. F. V. Atkinson, Discrete and continuous boundary problems, Mathematics in Science and Engineering, Vol. 8, Academic Press, New York-London, 1964. MR 0176141
  • 4. Antony Jameson, Solution of the equation 𝐴𝑋+𝑋𝐵=𝐶 by inversion of an 𝑀×𝑀 or 𝑁×𝑁 matrix, SIAM J. Appl. Math. 16 (1968), 1020–1023. MR 0234974
  • 5. Peter Lancaster, Explicit solutions of linear matrix equations, SIAM Rev. 12 (1970), 544–566. MR 0279115
  • 6. G. W. Stewart and R. H. Bartels, A solution of the equation $AX+XB=C$, Common. ACM 15, 1976, 820-826.
  • 7. K. N. Murty, K. R. Prasad and P. V. S. Anand, Two-point boundary value problems associated with Liapunov type matrix difference system, Dynam. Systems Appl. 4 (1995), 205-213. CMP 95:14

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 39A10, 34B05

Retrieve articles in all journals with MSC (1991): 39A10, 34B05

Additional Information

K. N. Murty
Affiliation: Department of Applied Mathematics, Andhra University, Visakhapatnam - 530 003, India

V. Lakshmi Prasannam
Affiliation: Department of Mathematics, Post Graduate Centre, P. B. Siddhartha College Of Arts & Science, Vijayawada - 520 010, India

Received by editor(s): April 17, 1996
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society