Iterative refinement of the solution of a positive definite system of equations
β Scribed by R. S. Martin; G. Peters; J. H. Wilkinson
- Book ID
- 105479418
- Publisher
- Springer-Verlag
- Year
- 1966
- Tongue
- English
- Weight
- 833 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0029-599X
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π SIMILAR VOLUMES
In this paper we investigate nonlinear matrix equations X Β± A \* X -q A = Q where q β₯ 1. We derive necessary conditions and sufficient conditions for the existence of positive definite solutions for these equations. We provide a sufficient condition for the equation X + A \* X -q A = Q to have two
In this paper we investigate some existence questions of positive semi-definite solutions for certain classes of matrix equations known as the generalized Lyapunov equations. We present sufficient and necessary conditions for certain equations and only sufficient for others.
In the present paper, we suggest two iteration methods for obtaining positive definite solutions of nonlinear matrix equation X -A'X-hA = Q, for the integer n >\_ 1. We obtain sufficient conditions for existence of the solutions for the matrix equation. Finally, some numerical examples to illustrate
## Abstract In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation __X__ + __A__^\*^__X__^βΞ±^__A__ = __Q__ with Ξ± β (0, β) are given. Iterative methods to obtain the positive definite solutions are established and the rat