Fast Recovery and Approximation of Hidden Cauchy Structure
Provides foundational algorithms for Cauchy matrix recovery and approximation, relevant to numerical linear algebra and signal processing.
The paper presents an optimal-complexity algorithm to determine if a matrix is Cauchy and exactly recover its defining points, and extends this to approximate Cauchy matrices from noisy data with proven bounds.
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.