A numerical algorithm to solveA^{T}XA - X = Q
- 1 October 1977
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 22 (5), 883-885
- https://doi.org/10.1109/tac.1977.1101604
Abstract
Two kinds of algorithms are usually resorted to in order to solve the well-known Lyapounov discrete equation A^{T}XA - X = Q : transformation of the original linear system in a classical one with n(n + 1)/2 unknowns, and iterative scheme [1]. The first requires n^{4}/4 storage words and a cost of n^{6}/3 multiplications, which is impractical with a large system, and the second applies only if A is a stable matrix. The solution proposed requires no stability assumption and operates in only some n 2 words and n 3 multiplications.Keywords
This publication has 4 references indexed in Scilit:
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- Comparison of numerical methods for solving Liapunov matrix equations†International Journal of Control, 1972
- A numerical solution of the matrix equation P = φ P φt+ SIEEE Transactions on Automatic Control, 1971
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