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Table 1

An example with 100 stars illustrating how the estimated velocity dispersion depends on the value of α.

α σu σv σw

True 10.000 15.000 7.000 22.000 14.000 10.000

0.0 10.090 14.775 7.083 21.712 13.636 9.783
0.5 10.033 14.808 7.090 21.610 13.638 9.902
1.0 10.032 14.806 7.091 21.429 13.619 10.041
1.5 10.031 14.805 7.093 21.251 13.604 10.182
2.0 10.029 14.804 7.094 21.076 13.591 10.324
10.0 10.015 14.824 7.143 18.587 13.845 12.819

Notes. In this case α = 0 would actually be used (no regularization). The solutions for α > 0 were only made to show that the velocity dispersion becomes more isotropic when regularization is used.

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