Mathematica Subroutines for Pivoting.  Execute the cells in this group to activate to subroutines.  

Mathematica Subroutine (Back Substitution).  Used after the pivoting strategy is used to reduce the matrix to upper-triangular form.

Mathematica Subroutine (No Pivoting Gaussian Elimination).  No row interchanges, i.e. no pivoting.

Mathematica Subroutine (Trivial Pivoting Gaussian Elimination).  If the diagonal element is zero, interchange the first non-zero element in the column below the diagonal.

Mathematica Subroutine (Partial Pivoting Gaussian Elimination).  The diagonal element is interchanged so that it is larger in magnitude than the elements in the column below it.

Mathematica Subroutine (Scaled Partial Pivoting Gaussian Elimination).  The diagonal element is interchanged so that it is larger in scaled magnitude than the scaled magnitude of the elements in the column below it.

Mathematica Subroutine (Total Pivoting Gaussian Elimination).  The diagonal element is interchanged so that it is larger in magnitude than the elements in the block below and to the right of  it.  Both rows and columns are interchanged in this subroutine.  This is also called "complete pivoting" or "maximal pivoting."

(c) John H. Mathews 2005