此函数使用带旋转的高斯消元法求解线性系统Ax=b。该算法概述如下: 1) 初始化一个置换向量r = [1, 2,...,n],其中r(i)对应于A中的第i行。 2) 对于k = 1,...,n-1,找到a(r(k),a(r(k+1),k),...,a(r(n),k)中最大的(绝对值)元素。 3) 假设r(j,k)是最大的元素,切换r(j)和r(k)。 4) 对于i=1,...,k-1,k+1,...,n计算:zeta = a(r(i),k) / a(r(k),k)。 5) 对于j=k,...,n,计算:a(r(i),j)=a(r(i),j)-a(r(k),j)*zeta,b(r(i)) = b(r(i))-b(r(k))*zeta。 6) 步骤1到6有效地对角化了A。 7) 解向量中的每个元素为:x(r(i)) = b(i)/a。
Gaussian Elimination with Partial Pivoting in MATLAB
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