On the existence of a positive definite solution of the matrix equation X+ATX−1A= I
✍ Scribed by Jacob C. Engwerda
- Book ID
- 107826579
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 852 KB
- Volume
- 194
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
The two matrix equations X s + A T X -t A = I n and X s -A T X -t A = I n are studied. Based on the fixed-point theory, the existence of the symmetric positive definite solutions are proved. Sensitivity analysis of the maximal solution is presented. Some elegant estimates of the positive definite so
The Hermitian positive definite solutions of the matrix equation X + A \* X -2 A = I are studied. A necessary and sufficient condition for existence of solutions is given in case A is normal. The basic fixed point iterations for the equation in case A is nonnormal with A are discussed in some detai
## Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation __X__ + __A__^\*^__X__^−α^__A__ = __Q__ with α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rat