The idea to detect singularities is to define smooth scalar functions which have regular
zeros at the singularity points. These functions are called test functions. Suppose we
have a singularity which is detectable by a test function
.
Also assume we have found two consecutive points
and
on the curve
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(23) |
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(24) |
Having found two points and
one may want to locate the point
where
vanishes. A logical solution is to solve the following system
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(25) |
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(26) |