采用近似计算获得行列式误差可控的值

Error-Controlled Values of Determinant Obtained by Approximate Calculation

众所周知,行列式的精确计算具有重要意义.然而,由于计算误差的积累与传播,使其成为一个具有挑战性的难题.对于元素中不含变元的任意一个行列式,基于高斯消元法,文章通过精确控制每一个中间运算的精度,提出控制其计算结果误差的一个数值算法.利用该算法,不论行列式是否病态,均可获得其任意精度的值.

It is well known that the accurate calculation of a determinant is of great significance. However, due to the accumulation and propagation of calculation errors,it has been a challenge. Based on Gaussian elimination method and by precisely controlling intermediate calculation accuracy, the paper proposes a numerical algorithm for controlling the result errors of the determinant whose entries do not contain any variable. With the algorithm, the value of the determinant can be obtained to arbitrary precision regardless of whether the determinant is ill-conditioned or not.