Properties of positive definite solutions of the equation X + A*X-2A = I1

Linear Algebra and Its Applications

Volumn 279, Issue 1-3, 1998, Pages 303-316

  Ivanov, Ivan G ^a   El Sayed, Salah M ^b  

^a SHUMEN UNIVERSITY   (Bulgaria)

^b BENHA UNIVERSITY   (Egypt)

Author keywords

Iterative method; Matrix equation; Positive definite solution

Indexed keywords

EID: 0043081344     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(98)00023-8     Document Type: Article

References (12)

1. -1B*, Linear Algebra Appl. 134 (1990) 53-62.
2. -1A = Q, Linear Algebra Appl. 186 (1993) 255-275.
3. TX-1 A = I, Linear Algebra Appl. 194 (1993) 91-108.
4. B.L. Buzbee, G.H. Golub, C.W. Nielson, On direct methods for solving Poisson's equations, SIAM J. Numer. Anal. 7 (1970) 627-656.
5. A.S. Housholder, The Theory of Matrices in Numerical Analysis, Blaisdell, New York, 1964.
6. M. Parodi, La localisation des valeurs caracteristiques des matrices et ses applications, Gauthier-Villars, Paris, 1959.
7. m)x = 0 (in Bulgarian), Ann. Sofia University Kl. Okhridski 72 (1978) 159-164.
8. J.H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, London, 1965.
9. M. Petkov, An iterative method for computing A (in Russian), Numerical Methods and Applications'84, Sofia, 1985.
10. M. Salah El-Sayed, The Study on Special Matrices and Numerical Methods for Special Matrix Equations, Ph.D. Thesis, Sofia, 1996.
11. P. Lancaster, Theory of Matrices, Academic Press, New York, 1969.
12. M. Salah El-Sayed, Theorems for the existence and computing of positive definite solutions for two nonlinear matrix equations, in: Proceedings of 25th Spring Conference of the Union of Bulgarian Mathematicians, Kazanlak, 1996.