PARTIAL PIVOTING

The existing values ​​in the main diagonal that result from the last operation will be called pivots. The Gaussian elimination with pivoting is applied to locate the numbers with the greatest value in absolute value in the positions aii, to do this, rows and columns are exchanged until the number with the highest absolute value in the corresponding positions of the diagonal is located.

 

In this method, the algorithm selects the entry with largest absolute value from the column of the matrix that is currently being considered as the pivot element.

Partial pivoting is generally sufficient to adequately reduce round-off error. However, for certain systems and algorithms, complete pivoting (or maximal pivoting) may be required for acceptable accuracy.