# Rate Constant Matrix Contraction Method for Stiff Master Equations with Detailed Balance

Source: [Rate Constant Matrix Contraction Method for Stiff Master Equations with Detailed Balance](<https://www.sota2.com/research/paper/68fa5b281e209131ce9c5e95>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:56:07.208Z

Authors: Satoru Iwata, Taihei Oki, Shinsaku Sakaue

Published: 2023-12-09T05:24:37.000Z

## Abstract

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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2312.05470>)

[PDF](<https://arxiv.org/pdf/2312.05470.pdf>)