Numerical Techniques for Singular Solutions and Positive‑dimensional Components

Due to the necessary ill-conditioning in small neighborhoods of singular solutions, special methods are used to perform numerical computations associated with singular solutions. This talk will summarize so-called deflation or regularization methods used in numerical algebraic geometry. It will conclude with a geometric description of a witness set, which is the data structure used in numerical algebraic geometry for representing positive-dimensional irreducible algebraic sets.