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

2021/10/07 by Peter Benner, Benner, Peter, Bruno Iannazzo +5
Computer Science · Engineering · #Advanced Adaptive Filtering Techniques #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Power System Optimization and Stability

paper · pdf · doi:10.48550/arxiv.2110.03254

openalex publication_date 2021/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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-NARE 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

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