Get an overview of the Gauss-Jordan method and elimination with our bite-sized video lesson! Master this concept with examples, then test your skill with a quiz.
D. Petkovic´, "Gauss-Jordan elimina- tion method for computing outer inverses," Applied Mathemat- ics and Computation, vol. 219, no. 9, pp. 4667-4679, 2013.Stanimirovic´ P S and Petkovic´ M D 2013 Gauss-Jordan elimination method for computing outer inverses. Appl. Math. Comput...
这里先给出一些铺垫:既然求逆,前提肯定是方阵A是可逆的,对矩阵A进行几种初等变换可以得到上三角矩阵U,假设分别经过了3种初等变换E,F,G最后得到U,那么A=GFEU,同时A总可以分解为一个下三角矩阵与一个上三角矩阵相乘,即A=LU,其中L为下三角矩阵,因此L=GFE。 当将A和E放在一起组成一个新的矩阵时,将A变化为...
Gauss-Jordan Elimination
intgauss_jordan(intn){//a为增广矩阵intr,w=0;for(inti=0;i<n&&w<n;w++,i++){//进行到第i列,第w行intr=w;for(intj=w+1;j<n;j++)if(fabs(a[j][i])>fabs(a[r][i]))r=j;//找到当前列绝对值最大的行if(fabs(a[r][i])<eps){w--;continue;}//当前列值都为0,跨过当前步if(...
The Gauss-Jordan elimination method starts the same way that the Gauss elimination method does, but then instead of back substitution, the elimination continues. The Gauss-Jordan method consists of: ▪ Creating the augmented matrix [A|b] ▪ Forward elimination by applying EROs to get an upper...
Solve the following system of linear equations by transforming its augmented matrix to reduced echelon form (Gauss-Jordan elimination). Find the vector form for the general solution. x1−x3−3x53x1+x2−x3+x4−9x5x1−x3+x4−2x5=1=3=1.x1−x3−3x5=13x1+x2−x3+x4−9x5...
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However, I am getting Wrong Answer. I think there is a bug in my implementation of Gauss Jordan Elimination (this is the first time I am coding that). Can somebody help me? Here is my code. typedeflongdoubledb;typedefvector<db>vd;typedefvector<vd>vvd;#defineEPS1e-9dbGaussJordan(vvd&A...
rrefimplements Gauss-Jordan elimination with partial pivoting. A default tolerance ofmax(size(A))*eps*norm(A,inf)tests for negligible column elements that are zeroed-out to reduce roundoff error. Extended Capabilities expand all Version History ...