2023/02/21 by Iannazzo, Bruno, Meini, Beatrice, Poloni, Federico
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2302.10604
By exploiting the connection between solving algebraic \top-Riccati equations and computing certain deflating subspaces of \top-palindromic matrix pencils, we obtain theoretical and computational results on both problems. Theoretically, we introduce conditions to avoid the presence of modulus-one eigenvalues in a \top-palindromic matrix pencil and conditions for the existence of solutions of a \top-Riccati equation. Computationally, we improve the palindromic QZ algorithm with a new ordering procedure and introduce new algorithms for computing a deflating subspace of the \top-palindromic pencil, based on quadraticizations of the pencil or on an integral representation of the orthogonal projector on the sought deflating subspace.