Quasi-Optimum Scaling of Symmetric Positive-Definite Matrices

摘要

Various approaches to scaling in overdetermined physical problems are considered. Trace invariance in scaling is imposed for the sake of definiteness. It is then shown that Marquardt's scaling to unit main diagonal leads to a maximum determinant. In a series of numerical experiments this sort of scaling is compared to the theoretical optimum. Results are reported which indicate that differences in condition of matrices scaled optimally and to unit main diagonal are computationally insignificant. A wider use of unit-diagonal scaling is recommended when treating positive-definite matrices. (Atomindex citation 16:086151)