高斯-若尔当消元法(Gauss-Jordan Elimination) 高斯消元法,是线性代数中的一个算法,可用来求解线性方程组,并可以求出矩阵的秩,以及求出可逆方阵的逆矩阵。高斯消元法的原理是:若用初等行变换将增广矩阵 化为 ,则AX = B与CX = D是同解方程组。 所以我们可以用初等行变换把增广矩阵转换为行阶梯阵,然后回代...
3)从而得到简化的三角方阵组,注意它更容易解 4)这时可以使用向后替换算法(Algorithm for Back Substitution)求解得z=-4/-4=1, y=4-2z=4-2=2, x= (1-y-z)/2=(1-2-1)/2=-1 总结上面过程,高斯消元法其实就是下面非常简单的过程 原线性方程组 ——> 高斯消元法 ——> 下三角或上三角形式的线...
3)从而得到简化的三角方阵组,注意它更容易解 4)这时可以使用向后替换算法(Algorithm for Back Substitution)求解得z=-4/-4=1, y=4-2z=4-2=2, x= (1-y-z)/2=(1-2-1)/2=-1 总结上面过程,高斯消元法其实就是下面非常简单的过程 原线性方程组 ——> 高斯消元法 ——> 下三角或上三角形式的线...
摘要 public class GaussElimination { public static void main(String[] args) { double[][] matrix = {{2, 1, -1, 8}, {-3, -1, 2, -11}, {-2, 1, 2, -3}}; // 3x4 matrix int n = matrix.length; // number of equations double[] x = new double[n]; // solution vector /...
Elimination(); BackSubstitution(); PrintRoot(); }//消元法publicstaticvoidElimination() { PrintA();for(intk = 0; k < n; k++) { WrapRow(k);for(inti = k+1; i < n; i++) {doublel = A[i][k] /A[k][k]; A[i][k]= 0;for(intj = k+1; j < n; j++) { ...
1. In the Gauss Elimination Method, which of the following steps is not included? Elimination of unknowns Elimination of unknowns Reduction to an upper triangular system Back substitution to find unknowns Cofactor evaluation Answer:Option d; The basic phases in Gauss Elimination are the elimination...
The Gauss elimination method consists of: ▪ creating the augmented matrix [A|b] ▪ applying EROs to this augmented matrix to get an upper triangular form (this is called forward elimination) ▪ back substitution to solve For example, for a 2× 2 system, the augmented matrix would be:...
Any factorization/back substitution scheme for the solution of linear systems consists of two phases which are different in nature, and hence may be inefficient for parallel implementation on a single computational network. The Gauss-Jordan elimination scheme unifies the nature of the two phases of ...
12 Gaussan Elimination12高斯消去法 1.2GaussianElimination Row-EchelonForm •In1.1,weworkedonmanipulatinganaugmentedmatrixusingelementaryrowoperationssothatourresultingequationscouldeasilybesolvedforthevaluesofthevariables.•OurGoalwastogettheaugmentedmatrixintoRow-EchelonForm:–Allzerorowsareatthebottom–The...
Back substitution of Gauss-Jordan calculator reduces matrix to reduced row echelon form. But practically it is more convenient to eliminate all elements below and above at once when using Gauss-Jordan elimination calculator. Our calculator uses this method. It is important to notice that while ...