Appears in collection : 2023 - T3 - WS2 - Geometry of polynomial system solving, optimization and topology

Numerical algebraic geometry provides a collection of algorithms for computing and analyzing solution sets of polynomial systems. This talk will discuss new techniques that have been developed in numerical algebraic geometry for focusing on real solution sets of polynomial systems. Several applications of these techniques will be presented such as computing smooth points on algebraic sets, approximate synthesis of mechanisms, and path planning for output mode switching.