An algorithm for simultaneous magnitude and phase approximation of bivariate rational polynomials (Q756357)

The authors consider the simultaneous magnitude and phase approximation of a continuous complex target T(z) by a complex rational polynomial R(p,z). The bivariate case is considered in detail. The problem can be formalized as the minimization with respect to p of the quantity \(\max_{z\in D}\{v_ 1| | T(z)| -| R(p,z)| |\), \(v_ 2| \arg [T(z)]-\arg [R(p,z)]| \}\), where \(D=\{(z_ 1,z_ 2):| z_ 1| <1\), \(| z_ 2| <1\}\), and \(v_ 1,v_ 2\) are real numbers. The stability and the convergence of the proposed algorithm are proved and its application is exemplified.