We introduce GPLS (Genetic Programming for Linear Systems) as a GP system that finds mathematical expressions defining an iteration matrix. Stationary iterative methods use this iteration matrix to solve a system of linear equations numerically. GPLS aims at finding iteration matrices with a low spectral radius and a high sparsity, since these properties ensure a fast error reduction of the numerical solution method and enable the efficient implementation of the methods on parallel computer architectures. We study GPLS for various types of system matrices and find that it easily outperforms classical approaches like the Gauss–Seidel and Jacobi methods. GPLS not only finds iteration matrices for linear systems with a much lower spectral radius, but also iteration matrices for problems where classical approaches fail. Additionally, solutions found by GPLS for small problem instances show also good performance for larger instances of the same problem.

我们引入 GPLS（线性系统的遗传规划）作为 GP 系统，它可以找到定义迭代矩阵的数学表达式。平稳迭代方法使用此迭代矩阵对线性方程组进行数值求解。GPLS 旨在找到具有低光谱半径和高稀疏度的迭代矩阵，因为这些特性确保了数值求解方法的快速误差减少，并能够在并行计算机体系结构上有效地实现这些方法。我们研究了各种类型的系统矩阵的 GPLS，发现它很容易胜过经典方法，如 Gauss-Seidel 和 Jacobi 方法。GPLS 不仅可以找到谱半径低得多的线性系统的迭代矩阵，还可以找到经典方法失败的问题的迭代矩阵。此外，