Representation of rational positive real functions of several variables by means of positive long resolvent

2021/03/03 by M. F. Bessmertnyĭ, Bessmertnyi, M. F.
Computer Science · Mathematics · #15A22 (Primary) 94C05 (Secondary) #Advanced Optimization Algorithms Research #Complex Variables (math.CV) #FOS: Mathematics #Matrix Theory and Algorithms #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2103.02541

openalex publication_date 2021/03/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

A rational homogeneous (of degree one) positive real matrix-valued function is presented as the Schur complement of a block of the linear pencil with positive semidefinite matrix coefficients. The partial derivative numerators of a rational positive real function are the sums of squares of polynomials.

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