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I'm a new user of BLAS/Lapack, and I'm just wondering is there a routine which does Gaussian elimination or even Gaussian-Jordan elimination? I googled and looked at their documentations, but still couldn't find them.
Thanks a lot for helping me out!
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(1) Write the given system of linear equations in matrix form AX = B, where A is the coefficient matrix, X is a column matrix of unknowns and B is the column matrix of the constants. (2) Reduce the augmented matrix [A : B] by elementary row operations to get [A' : B']. (3) We get A' as an upper triangular matrix.
To perform Gauss-Jordan Elimination: Swap the rows so that all rows with all zero entries are on the bottom. Swap the rows so that the row with the largest, leftmost nonzero entry is on top. Multiply the top row by a scalar so that top row's leading entry becomes 1.
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of operations performed on the corresponding matrix of coefficients.
The following three types of elementary row operations are performed on a matrix using the Gauss elimination method: Type 1: Two rows are swapped. Type 2: A row is multiplied by a nonzero number. Type 3: A multiple of one row is added to another row.
Gaussian elimination is basically the same as LU factorization. The routine xGETRF computes the LU factorization (e.g., DGETRF for real double precision matrices). The U factor corresponds to the matrix after Gaussian elimination. The U factor is stored in the upper triangular part (including the diagonal) of the matrix A on exit.
LU factorization / Gaussian elimination is commonly used to solve linear systems of equations. You can use the xGETRS routine to solve a linear system once you have computed the LU factorization.
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