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.

翻译：本文提出了加速雅可比矩阵对角化方法的新颖途径，具体通过将大规模矩阵对角化建模为半马尔可夫决策过程，并将小规模矩阵对角化建模为马尔可夫决策过程。此外，我们探讨了在不同尺寸矩阵间构建可扩展架构的潜力。在短期训练过程中，我们的方法显著减少了对角化所需的步骤数，并展现出高效的推理能力。值得注意的是，该方法展现出向大规模矩阵扩展的可能性，表明其具有广泛应用的潜力。训练完成后，我们获得了动作-状态概率与状态转移图，这些图表征了不同状态间的转换关系。这些输出不仅揭示了对角化过程的内在机制，还为大规模矩阵相关计算成本的节约开辟了路径。本研究的进展提升了矩阵对角化的效率与可扩展性，为科学和工程领域实际应用中的部署创造了新的可能性。