中文摘要：

利用三对角线性方程组追赶法思想，推导出五对角线性方程组追赶法，理论推导表明：对于n阶五对角线性方程组求解，该算法的运算量级为O（11n），数值实验表明：该算法比高斯消去法和其他一些迭代法有明显的速度和内存优势，这极大地提高了解线性方程的速度。

英文摘要：

A forward elimination and backward substitution algorithm was derived for solutions of linear equations system with quinary diagonal matrix using ones with triune diagonal matrix. It is deduced theoretically that the operational amount is O（11n） for a linear equation system with quinary diagonal matrix whose order is n. It is shown in the numerical experiments that this method has some advantages in computational cost and memory need evidently. It improves the calculational rates.