用旋转法消除高斯软件

Function uses Gauss elimination with pivoting to solve a linear system in standard format.

软件应用简介

This function solves a linear system Ax=b using the Gaussian elimination method with pivoting. The algorithm is outlined below: 

1) Initialize a permutation vector r = [1, 2,…,n] where r(i) corresponds to row i in A. 

2) For k = 1,…,n-1 find the largest (in absolute value) element among a(r(k),k),a(r(k+1),k),…,a(r(n),k). 

3) Assume r(j,k) is the largest element. Switch r(j) and r(k). 

4) For i=1,…,k-1,k+1,…,n calculates: 

zeta = a(r(i),k) / a(r(k),k) 

5) For j=k,…,n calculate: 

a(r(i),j)=a(r(i),j)-a(r(k),j)*zeta 

b(r(i)) = b(r(i))-b(r(k))*zeta 

6) Steps 1 through 6 has effectively diagonalized A. 

7) Each element in the solution vector is: 

x(r(i)) = b(i)/a(i,i);

界面展示

结果示意

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