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**the condition of the homotopy:**
- This global parameter can be used to tune the parameters
according to the general expectancy of how difficult the
solution paths will be.
Low values of this parameter lead to a loose path tracking,
whereas higher values tighten up the path-following.
**number of paths tracked simultaneously:**
- In simultaneous path-following ,
the same discretization for the
values of the continuation parameter is used for a number of paths.
Clustering of solution paths is checked during continuation for
the number of paths that are followed simultaneously.
In sequential path-following ,
i.e., when this parameter equals one,
the step sizes are adjusted according to the difficulty of the
current path being followed. In this case, a difficult path does
not slow down the continuation for the other ones.
**maximum number of steps along a path:**
- This parameter bounds the amount of work along a solution path.
Continuation for the path being followed stops when
the number of steps exceeds this threshold value.
**distance from target to start end game:**
- Tracking solution paths is organized in two stages.
As
*t*<1, no singularities are likely to occur and paths can be
tracked more loosely. When , paths may converge
to singular solutions
or diverge to infinity , so they have to be
tracked more carefully. This distance marks the switch towards
the second stage, that is the so-called end game .
**order of extrapolator in end game:**
- The direction of a diverging solution path provides a normal to
a face of the system that certificates the deficiency.
In this polyhedral end game ,
extrapolation is used to determine
winding numbers .
When the order of the extrapolator equals zero, then the polyhedral
end game is turned off.
**maximum number of re-runs:**
- Solution paths may be clustered at the end of the continuation.
If the number of re-runs is higher than one, then clustered solution
paths are re-computed by following the paths more closely.
Setting this value to zero turns off this facility.

** Next:** Adaptive step-size control
** Up:** Polynomial Continuation
** Previous:** Polynomial Continuation
*Jan Verschelde*

*3/7/1999*