### Multiple test functions

The above is a general way to detect and locate singularities depending on one test function. However, it may happen that it is not possible to represent a singularity with only one test function.

Suppose we have a singularity which depends on test functions. Also assume we have found two consecutive points and and all test functions change sign:

| (27)

Also assume we have found, using a one-dimensional secant method, all zeros of the test functions. In the ideal (exact) case all these zeros will coincide:

| (28)

Since the continuation is not exact but numerical, we cannot assume this. However, the locations of probably will be clustered around some center point . In this case we will glue the points to .

A cluster will be detected if for some small value . In this case we define as the mean of all located zeroes:

| (29)