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Many problems give rise to polynomial systems. These systems often haveseveral parameters and we are interested to study how the solutions vary whenwe change the values for the parameters. Using predictor-corrector methods wetrack the solution paths. A point along a solution path is critical when theJacobian matrix is rank deficient. The simplest case of quadratic turningpoints is well understood, but these methods no longer work for general typesof singularities. In order not to miss any singular solutions along a path wepropose to monitor the determinant of the Jacobian matrix. We examine theoperation range of deflation and relate the effectiveness of deflation to thewinding number. Computational experiments on systems coming from differentapplication fields are presented.

Sweeping Algebraic Curves for Singular Solutions