SpectrUW: A laboratory for the numerical exploration of spectra of linear operators

Spectra of linear operators play an important role in various aspects of applied mathematics. For all but the simplest operators, the spectrum cannot be determined analytically and as such it is difficult to build up any intuition about the spectrum. One way to obtain such intuition is to consider many examples numerically and observe emerging patterns. This is feasible using an efficient black-box numerical method, i.e., a method that requires no conceptual changes for different examples. Hill’s method satisfies these requirements. It is the mathematical foundation of SpectrUW (pronounced “spectrum”), mathematical black-box software that serves as a laboratory for the numerical approximation of spectra of one-dimensional linear operators.