706 research outputs found
Fast Recovery and Approximation of Hidden Cauchy Structure
We derive an algorithm of optimal complexity which determines whether a given
matrix is a Cauchy matrix, and which exactly recovers the Cauchy points
defining a Cauchy matrix from the matrix entries. Moreover, we study how to
approximate a given matrix by a Cauchy matrix with a particular focus on the
recovery of Cauchy points from noisy data. We derive an approximation algorithm
of optimal complexity for this task, and prove approximation bounds. Numerical
examples illustrate our theoretical results
- …