Figure 1a: Sensitivity of zeros for coefficients -1/1 -
The zeros colored by their
sensitivity to variation in the coefficients of the polynomial. The
sensitivity is cumulative over all the coefficients. The color scale
represents a normalized sensitivity to the range of values; red is
insensitive to violet which is strongly sensitive. All zeros are pictured.
The zeros are for coefficients -1 and +1 for polynomial degree 17.
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Figure 1b: Density of zeros for coefficients -1/1 -
The zeros are colored by their
density. The distribution of zeros has been coarsened by collecting
them onto a grid, resulting in a slight blockiness. The range of
color is normalized to the range of densities; red is low density to
blue which is high density.
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Figure 1c: Sensitivity of zeros relative to coefficient a1 -
Figure 1a is reproduced, this time with conditioning relative to the
coefficient for x.
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Figure 1d: Sensitivity of zeros relative to coefficient a9 -
Figure 1a is reproduced, this time with conditioning relative to the
coefficient for x9.
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Figure 1e: Sensitivity of zeros relative to coefficient a16 -
Figure 1a is reproduced, this time with conditioning relative to the
coefficient for x16.
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