The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this work, we aim to further accelerate the rate of convergence by introducing a preconditioning technique. After constructing the preconditioner, we preprocess the progressive iterative approximation (PIA) and its variants, called the preconditioned GIMs. We show that the proposed preconditioned GIMs converge and the extra computation cost brought by the preconditioning technique is negligible. Several numerical experiments are given to demonstrate that our preconditioner can accelerate the convergence rate of PIA and its variants.

翻译：在数据插值/拟合中，几何迭代法（GIM）被广泛应用，但其收敛速度缓慢，影响计算效率。最近，文献中已经做了很多工作来保证GIM的加速。 在本文中，我们旨在通过引入预处理技术进一步加快收敛速度。构造完预处理器后，我们对渐进迭代逼近（PIA）及其变体进行了预处理，称为预处理GIM。 我们证明了所提出的预处理GIM收敛，预处理技术带来的额外计算成本可忽略不计。 给出了几个数值实验，证明了我们的预处理器可以加速PIA及其变体的收敛速度。