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

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