Let A/sub m/ be an m/spl times/m principal submatrix of an infinite-dimensional matrix A. We give a simple formula which expresses A/sub m+1//sup /spl minus/1/ in terms of A/sub m//sup /spl minus/1/, and based on this formula, an algorithm which computes the inverses of A/sub m/ for m=1, 2, 3, ..., n using only 2n/sup 3//spl minus/2n/sup 2/+n arithmetic operations. This is an improvement over the naive method of computing the inverses separately which would require /spl Sigma//sub m=1//sup n/ m/sup 3/=O(n/sup 4/) arithmetic operations.
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机译：令A / sub m /为无限维矩阵A的m / spl次/ m主子矩阵。我们给出一个简单的公式，用A表示A / sub m + 1 // sup / spl minus / 1 / / sub m // sup / spl minus / 1 /，并基于此公式，该算法仅使用2n / sup计算m = 1、2、3，...，n的A / sub m /的反函数3 // spl负/ 2n / sup 2 / + n算术运算。这是对分别计算逆的天真的方法的改进，后者仅需要/ spl Sigma // sub m = 1 // sup n / m / sup 3 / = O（n / sup 4 /）算术运算。
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