Homotopies to solve Multilinear Systems

Abstract:

Many applications in mechanism design lead to structured polynomial systems. For systems where only isolated solutions matter, homotopies that exploit multihomogeneous structures are well developed. For mechanisms that move, computing the corresponding algebraic curves with a optimal number of solution paths requires an adaption of the numerical representation for these curves. In the line of our work, we report on our new algorithms to solve multilinear systems more efficiently.

Joint work with Yun Guan.

ILAS 2010, 16th Conference of the International Linear Algebra Society, minisymposium on Applications of Linear and Multilinear Algebra in Life Sciences and Engineering, Palazzo dei Congressi, Pisa, Italy, 21-25 June 2010.

slides of the talk