In this paper, we introduce innovative approaches for accelerating the Jacobi method for matrix diagonalization, specifically through the formulation of large matrix diagonalization as a Semi-Markov Decision Process and small matrix diagonalization as a Markov Decision Process. Furthermore, we examine the potential of utilizing scalable architecture between different-sized matrices. During a short training period, our method discovered a significant reduction in the number of steps required for diagonalization and exhibited efficient inference capabilities. Importantly, this approach demonstrated possible scalability to large-sized matrices, indicating its potential for wide-ranging applicability. Upon training completion, we obtain action-state probabilities and transition graphs, which depict transitions between different states. These outputs not only provide insights into the diagonalization process but also pave the way for cost savings pertinent to large-scale matrices. The advancements made in this research enhance the efficacy and scalability of matrix diagonalization, pushing for new possibilities for deployment in practical applications in scientific and engineering domains.

本文介绍了加速矩阵对角化的创新方法，其中大型矩阵对角化采用了半马尔可夫决策过程，小型矩阵对角化则采用了马尔可夫决策过程。我们考察了在不同大小的矩阵之间利用可扩展架构的潜力。在短时间内，我们的方法发现了对角化所需步骤的显著减少，并表现出高效的推理能力。重要的是，这种方法展示了对大规模矩阵的可扩展性，表明其在科学和工程领域具有广泛的应用潜力。在训练完成后，我们获得了动作-状态概率和转移图，这些图描述了不同状态之间的转换。这些输出不仅能够深入了解对角化过程，还为大规模矩阵相关的成本节约铺平了道路。本研究的进展提高了矩阵对角化的效能和可扩展性，推动在科学和工程领域实际应用中的新可能性。

基于图同构网络和AlphaZero框架的矩阵对角化加速