Multi-shift quadratic alternating direction implicit iteration for high-speed positive-real balanced truncation

This paper presents a multi-shift generalization of the recently proposed quadratic alternating direction implicit (QADI) iteration. QADI and its Cholesky factor (CF) variant, CFQADI, have been shown to be efficient ways of solving the large-scale algebraic Riccati equations (AREs) required in positive-real balanced truncation (PRBT). However, only their single-shift implementations have been considered so far. Using linear fractional transformation (LFT), we present elegant multi-shift extensions of both QADI and CFQADI, thereby enabling even faster and more accurate PRBT.