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By scaling the coefficients are transformed so that they
do not have extreme values. The purpose is to avoid numerical problems.
- Equation Scaling
- means that every
polynomial is divided by its average coefficient.
- Variable Scaling
- uses transformations
like z = (2c) x.
The transformation is such that real solutions remain real.
The inverse of the condition number of the linear system that is solved
to set up this transformation gives an indication on the condition of
the original polynomial system.
- Solution Scaling
- transforms the solutions
of a scaled system back into the original coordinate system. Note that
in the original coordinates, the solutions can be ill-conditioned.