We introduce an adaptive finite element method for computing electromagnetic guided waves in a closed, inhomogeneous, pillared three-dimensional waveguide at a given frequency based on the inverse ...

The l₂ normalized inverse, shifted inverse, and Rayleigh quotient iterations are classic algorithms for approximating an eigenvector of a symmetric matrix. This work establishes rigorously that each ...

Dozens of machine learning algorithms require computing the inverse of a matrix. Computing a matrix inverse is conceptually easy, but implementation is one of the most difficult tasks in numerical ...

Topological methods offer a rigorous mathematical framework that underpins modern approaches to inverse scattering and imaging. By quantifying the sensitivity of a misfit or cost functional to ...

Absolute value equations (AVEs), characterised by the inclusion of absolute value functions in the variables, present inherently non‐smooth and computationally challenging problems that are often ...

Dr. James McCaffrey from Microsoft Research presents a complete end-to-end demonstration of computing a matrix inverse using the Newton iteration algorithm. Compared to other algorithms, Newton ...