Title :
A numerical algorithm to solve AT X A - X = Q
Author_Institution :
Ecole Nationale Sup??rieure d´Electrotechnique et de G??nie Physique, Grenoble C??dex, France
Abstract :
Two kinds of algorithm are usually resorted to in order to solve the well-known Lyapounov discrete equation AT X A - 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 n4/4 storage words and a cost of n6/3 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 n2 words and n3 multiplications.
Keywords :
Costs; Eigenvalues and eigenfunctions; Equations; Instruction sets; Iterative algorithms; Iterative methods; Linear systems; Matrices; Modular construction;
Conference_Titel :
Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications, 1977 IEEE Conference on
Conference_Location :
New Orleans, LA, USA
DOI :
10.1109/CDC.1977.271607
