This work was originally published by the author in 1999 in a book [1] and later became part of the author's doctoral thesis in 1999 [2]. Since the original language of these works is not English, the author provides a translation of the key ideas of these publications in this work. In addition, the chapter related to numerical experiments was recalculated on modern computers and using contemporary benchmark datasets. This article presents a novel approach to solving Hartree-Fock equations using Toeplitz and tensor matrices and bases based on regular finite elements. The issues discussed include the choice of basis, the dependence of data volume and number of arithmetic operations on the number of basis functions, as well as the arithmetic complexity and accuracy of computing two- and four-center integrals. The approach has been implemented in a software package, and results have been obtained that are in good agreement with theory.

翻译：本文作者于1999年在著作[1]中首次发表相关工作，后于1999年纳入其博士论文[2]。由于原著作非英语撰写，作者在此提供其中核心思想的英文译本。此外，与数值实验相关的章节已使用现代计算机和当代基准数据集重新计算。本文提出了一种利用Toeplitz矩阵和张量矩阵以及基于正则有限元基函数的哈特里-福克方程求解新方法。讨论的问题包括基函数的选择、数据量与算术运算次数对基函数数量的依赖关系，以及双中心和四中心积分计算的算术复杂度和精度。该方法已在软件包中实现，所得结果与理论吻合良好。