Heuristic parameter choice rule for solving linear ill-posed integral equations in finite dimensional space

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...