Ill-conditioned eigenvalues and polynomial roots:

theory and computation

 

Abstract

Defective eigenvalues and multiple polynomial roots are nearly impossible to compute numerically with standard methods. Many polynomials and matrices with well separated roots/eigenvalues are also extremely sensitive to rounding errors in numerical computation, such as the famous Wilkinson polynomial. In this talk we present unconventional perspective and approaches on those ill-conditioned problems. We shall show that, with deeper understanding, many ill-conditioned problems are well behaved and can be solved with high accuracy.