Matrix diagonalization is at the cornerstone of numerous fields of scientific computing. Diagonalizing a matrix to solve an eigenvalue problem requires a sequential path of iterations that eventually reaches a sufficiently converged and accurate solution for all the eigenvalues and eigenvectors. This typically translates into a high computational cost. Here we demonstrate how reinforcement learning, using the AlphaZero framework, can accelerate Jacobi matrix diagonalizations by viewing the selection of the fastest path to solution as a board game. To demonstrate the viability of our approach we apply the Jacobi diagonalization algorithm to symmetric Hamiltonian matrices that appear in quantum chemistry calculations. We find that a significant acceleration can often be achieved. Our findings highlight the opportunity to use machine learning as a promising tool to improve the performance of numerical linear algebra.

翻译：矩阵对角化是众多科学计算领域的基石。通过求解特征值问题实现矩阵对角化，需要一系列迭代步骤，最终使所有特征值和特征向量达到充分收敛且精确的解。这一过程通常伴随着高昂的计算成本。本文展示了如何利用基于AlphaZero框架的强化学习，通过将最快求解路径的选择视为棋盘游戏，从而加速雅可比矩阵对角化过程。为验证方法的可行性，我们将雅可比对角化算法应用于量子化学计算中出现的对称哈密顿矩阵。研究发现，该方法通常能够实现显著的加速效果。这一发现凸显了将机器学习作为数值线性代数性能提升工具的巨大潜力。