Separation procedure and new derivation of Larin's algorithms for solving algebraic Riccati equations

With the help of constructing orthogonal projections a transformation of a matrix into the block triangular form separating its spectrum into the "stable" and "unstable" parts is obtained. Using this form a modification of Larin's separation procedure is given. A new simple derivation of Larin's algorithms for construction of orthogonal projections and stabilizing solutions of matrix algebraic Riccati equations is produced. A high precision computer realisation of Larin's algorithms is created using Turbo C on IBM PCs and close compatibles.<>