Revised Version for TCAD 3015 Fast Positive-Real Balanced Truncation Via Quadratic Alternating Direction Implicit Iteration

Balanced truncation (BT), as applied to date in model order reduction (MOR), is known for its superior accuracy and computable error bounds. Positive-real balanced truncation (PRBT) is a particular BT procedure that preserves passivity and stability, and imposes no structural constraints on the original state space. However, PRBT requires solving two algebraic Riccati equations (AREs), whose computational complexity limits its practical use in large-scale systems. This paper introduces a novel quadratic extension of the alternating direction implicit (ADI) iteration, called QADI, that efficiently solves an ARE. A Cholesky factor version of QADI, called CFQADI, exploits lowrank matrices and further accelerates PRBT.