追赶法在求解循环和拟循环三对角方程组中的一种推广

An Extension of Chasing Method for Solving Circular and Quasi-Circular Tridiagonal Systems

针对循环或者拟循环三对角方程组,仿照追赶法的思想,给出了一种求解这两类方程组的追赶算法.该算法在求解循环和拟循环三对角方程组时用到的乘法和除法运算次数仅为8N和3N次,与传统计算循环三对角方程组的算法相比,提高了计算效率.数值试验表明,对于百万至千万阶的拟三对角方程组,本算法都可以在几秒内给出准确结果.

Based on the idea of chasing method, a new algorithm is developed to solving the circular and quasi-circular tridiagonal systems in this paper. The computational costs of multiplication and division are 8N and 3N, respectively. Compared with the traditional method, the new chasing method saves the computational cost. The numerical experiments indicate that, the exact solutions can be obtained in several seconds by using this method.