Using covariance extension equation to solve the Nevanlinna-Pick interpolation with degree constraint

TL;DR

This paper introduces a robust and efficient continuation method based on the covariance extension equation to solve the Nevanlinna-Pick interpolation problem with degree constraints, improving upon existing algorithms.

Contribution

It presents a new continuation-based approach that avoids initial value calculation for Nevanlinna-Pick interpolation with degree constraints, enhancing robustness and simplicity.

Findings

Method is robust and efficient in numerical tests

Avoids initial value calculation in the algorithm

Demonstrates effectiveness through a numerical example

Abstract

Nevanlinna-Pick interpolation problem has been widely studied in recent decades, however, the known algorithm is not simplistic and robust enough. This paper provide a new method to solve the Nevanlinna-Pick interpolation problem with degree constraint. It is based on the covariance extension equation proposed by Byrnes and Lindquist. A reformulation of the Nevanlinna-Pick interpolation problem is achieved and then solved by continuation method. This method need not calculate the initial value and a numerical example illustrates robustness and effciency of the proposed procedure