Three various pivoting strategies are partial pivoting, scaled partial pivoting and complete pivoting.
For partial or column pivoting, rearrange the rows of the matrix and the right-hand side to bring the numerically largest value in the column onto the diagonal. Through the process of partial pivoting, get the smallest possible quantities for the elimination process. As a consequence, no quantity is larger than 1 in magnitude which minimizes the chance of large errors. This is the most common method of pivoting as this is the fastest than all other pivoting methods.
Scaled partial pivoting is used in case of large variations in magnitude of the elements within a row by defining a scale factor for each row. The effect of scaling is to ensure that the largest element in each row has a relative magnitude of 1 before the comparison for row interchange is performed.
For complete pivoting, scan for the largest value in the entire sub-matrix instead of just the next column. This requires both row and column interchanges. Theoretically complete pivoting is more reliable than partial pivoting as it can be used with singular matrices. But, encountering a rank deficient matrix in numerical linear algebra is very rare. Due to which, complete pivoting does not consistently produce more accurate results than partial pivoting.