David Bindel, assistant professor of computer science, and Amanda Hood, a Ph.D. candidate working in the Cornell Center for Applied Mathematics, have received the 2015 SIAG/Linear Algebra Prize for their paper “Localization Theorems for Nonlinear Eigenvalue Problems,” which has also been selected by the Society for Industrial and Applied Mathematics (SIAM) as a SIGEST paper to be reprinted in the December 2015 SIAM Review. The paper was first published in SIAM Journal on Matrix Analysis and Applications in 2013.

The 2015 SIAG/Linear Algebra Prize goes to the authors of the most outstanding paper on a topic in applicable linear algebra published in English in a peer-reviewed journal within the three calendar years preceding the year of the award. Selection as a SIGEST paper for SIAM Review is another major recognition in the field.

Eigenvalues represent the frequency and damping of vibrations, and they are important in understanding mathematical models of how physical systems – from a highway bridge to an electronic circuit to a musical instrument – will behave dynamically in response to outside forces. Mathematicians have developed ways to analyze eigenvalue problems as long as the system is “linear” – changing smoothly in direct proportion to changes in frequency. The Cornell authors show how to apply these methods to more complex situations that often arise in the real world.

Bindel and Hood’s SIAG citation reads, “This extremely well-written paper shows how to extend localization results for linear eigenvalue problems to nonlinear eigenvalue problems, providing new insight into this important, challenging class of models.” The problem is considered so important that several mathematicians have challenged their colleagues to come up with a solution.