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- The polynomial has m very close roots around -1/a.
- For n=20,m=3,a=100i, there are 3 roots close to -1/100 i,
matching in the first 13 digits. Their condition numbers are greater
than so that at least 38 digits of working precision are needed
for isolating the roots. The remaining roots are well conditioned and
15 digits of working precision are sufficient to isolate them.
- Difficult situations can be obtained by tuning n,m and |a|.
- Interesting situations are: the case of
large degree and small cluster, i.e., n=100,500, m=3, a=100 i;
the case of large degree and large cluster, i.e., n=100,500, m=31,
a=1000.