This paper considers master equations for Markovian kinetic schemes that possess the detailed balance property. Chemical kinetics, as a prime example, often yields large-scale, highly stiff equations. Based on chemical intuitions, Sumiya et al. (2015) presented the rate constant matrix contraction (RCMC) method that computes approximate solutions to such intractable systems. This paper aims to establish a mathematical foundation for the RCMC method. We present a reformulated RCMC method in terms of matrix computation, deriving the method from several natural requirements. We then perform a theoretical error analysis based on eigendecomposition and discuss implementation details caring about computational efficiency and numerical stability. Through numerical experiments on synthetic and real kinetic models, we validate the efficiency, numerical stability, and accuracy of the presented method.

翻译：本文研究具有细致平衡性质的马尔可夫动力学体系的Master方程。以化学动力学为例，此类方程往往呈现大规模、高度刚性的特征。基于化学直觉，Sumiya等人(2015)提出了速率常数矩阵压缩(RCMC)方法，用于计算此类难解系统的近似解。本文旨在为RCMC方法建立数学基础。我们从若干自然需求出发，通过矩阵计算视角给出了RCMC方法的重新表述，并推导出该方法。随后，基于特征分解进行了理论误差分析，讨论了兼顾计算效率与数值稳定性的实现细节。通过合成模型与真实动力学模型的数值实验，验证了所提方法的效率、数值稳定性及精度。