Scaling

The pre-solution transformation of the data of a problem that attempts to make the magnitudes of all the data as close as possible. Such scaling is important for mathematical-and linear-programming problems as it helps to reduce roundoff error. Most mathematical-programming systems have a SCALE command that automatically adjusts the magnitudes of the data in the rows and columns. This can be done by multiplying the technological coefficient matrix Av by suitable row and column transformation matrices. A frequently used scaling algorithm is to divide each row by the largest absolute element in it, and then divide each resulting column by the largest absolute element in it. This ensures that the largest absolute value in the matrix is 1.0 and that each column and row has at least one element equal to 1.0.