A new heuristic parameter choice rule is proposed, which is an important process in solving the linear ill-posed integral equation. Based on multiscale Galerkin projection, we establish the error upper bound between the approximate solution obtained by this rule and the exact solution. Under certain conditions, we prove that the approximate solution obtained by this rule can reach the optimal convergence rate. Since the computational cost will be very large when the dimension of space increases, we analyze a special $m$-dimensional integral operator that can be transformed to $m$ one-dimensional integral operator, which can reduce the computational cost greatly. Numerical experiments show that the proposed heuristic rule is promising among the known heuristic parameter choice rules.

提出了一种新的启发式参数选择规则，这是求解线性不适定积分方程的一个重要过程。基于多尺度伽辽金投影，我们建立了该规则得到的近似解与精确解之间的误差上限。在一定条件下，我们证明了通过该规则得到的近似解可以达到最优收敛速度。由于空间维数增加时计算成本会非常大，我们分析一个特殊的$米$-维积分运算符，可以转换为 $米$一维积分算子，可以大大降低计算成本。数值实验表明，在已知的启发式参数选择规则中，所提出的启发式规则是有前途的。