Gauss-Jordan Total Pivoting

Linear Algebra and the C Language · Wikibooks

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    From Wikibooks, under CC BY-SA 4.0, as the source states it. This page at Wikibooks.

    Gauss-Jordan Total Pivoting (TP)

    Gaussian elimination, is an algorithm for solving systems of linear equations...Wikipedia: Gaussian elimination

    In this algorithm, Gauss-Jordan Total Pivoting, the pivot chosen is the largest absolute value found in a matrix. For this we perform row and column exchanges.

    To initialize the matrix Ab you must use the function: 

    double **Ab = i_Abr_Ac_bc_mR(RAb, CA, Cb));

    The function: gj_TP_mR();

    Solve: Ax = b

    Code study

    The function: gj_TP_mR(double **Ab);

    The function: sort_c_mR(double **Ab);

    • c00b.c
    • The function puts the columns in the correct order.
    • c00c.c

    The function: sort_r_mR(double **Ab);

    • c00d.c
    • The function puts the rows in the correct order.
    • c00e.c

    The function: gj1_T_mR(double **Ab);

    • c00f.c
    • The function selects the best pivot and puts zero under the pivot.
    • c00g.c
    • The function puts zero above the pivot.
    • c00h.c

    Applications

    Solve: A|x1|x2| ... |xn| = b1|b2| ... |bn|

    Compute the inverse of A: A|ID -> ID|InvA