Palindromic linearization and numerical solution of nonsymmetric algebraic T -Riccati equations

We identify a relationship between the solutions of a nonsymmetric algebraic T -Riccati equation ( T -NARE) and the deflating subspaces of a palindromic matrix pencil, obtained by arranging the coefficients of the T -NARE. The interplay between T -NAREs and palindromic pencils allows one to derive both theoretical properties of the solutions of the equation, and new methods for its numerical solution. In particular, we propose methods based on the (palindromic) QZ algorithm and the doubling algorithm, whose effectiveness is demonstrated by several numerical tests.