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Home MathPack Matrix Classes TIntMatrix, TMatrix and TMat3D Methods Balance
See also: Norm 

Balance

Unit: SDL_matrix
Class: TMatrix
Declaration: function Balance (Tolerance: double): boolean;

The function Balance performs a similarity transformation on the matrix such that the row and the column norms become approximately equal. This transformation normally improves the eigenvalue accuracy. The parameter Tolerance determines the tolerance to which the edge vectors are equalized. Tolerance is automatically limited to the range between 1.000001 and 1.050000 which comes to a relative tolerance of 0.0001% to 5%.

The function returns a TRUE value if the matrix is a square matrix and the maximum number of iterations is not reached. In all other cases a FALSE value is returned.

Remark: Balancing of a matrix may destroy the matrix properties under certain conditions (i.e. if a matrix contains small elements generated by roundoff errors). Thus balancing should be used with care.


Last Update: 2025-Sep-15