  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.
