A relative error bound for balanced stochastic truncation

Abstract

Recently, several methods have appeared for the approximation of (power) spectra, notably balanced stochastic truncation (BST). It is shown that BST satisfies a relative error bound approximately twice the bound for the relative error method (REM) proper. This offers a quantitative basis for the observation that BST and REM produce similar reduced-order models. Balanced stochastic truncation can therefore be interpreted as providing a computationally simple algorithm for relative error approximation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>