Hg. Xu et Lz. Lu, PROPERTIES OF A QUADRATIC MATRIX EQUATION AND THE SOLUTION OF THE CONTINUOUS-TIME ALGEBRAIC RICCATI EQUATION, Linear algebra and its applications, 222, 1995, pp. 127-145
We discuss some properties of a quadratic matrix equation with some re
strictions, then use these results on the algebraic Riccati equation t
o get a new algorithm. The algorithm sufficiently takes account of the
structure of the associated matrix; hence it is very effective.