Perron-Frobenius Theory and the Zeros of Polynomials

Perron-frobenius Theory and the Zeros of Polynomials

1. J. Douglas, Jr. and T. M. Gallie, An approximate solution of an improper boundary value problem, Duke Math. J. vol. 26 (1959) pp. 339-347. 2. F. John, Numerical solution of the equation of heat conduction for preceding times, Ann. Mat. Pura Appl. ser. IV vol. 40 (1955) pp. 129-142. 3. C. Pucci, Sui problemi di Cauchy non "ben posti," Atti Accad. Naz. Lincei. Rend. Cl. Sei. Fis. Mat. Nat. vol...

A primer of Perron–Frobenius theory for matrix polynomials

We present an extension of Perron–Frobenius theory to the spectra and numerical ranges of Perron polynomials, namely, matrix polynomials of the form L(λ) = Iλ − Am−1λm−1 − · · · − A1λ− A0, where the coefficient matrices are entrywise nonnegative. Our approach relies on the companion matrix linearization. First, we recount the generalization of the Perron–Frobenius Theorem to Perron polynomials ...

Laguerre polynomials and Perron-Frobenius operators

Sampling zeros and the Euler-Frobenius polynomials

In this paper, we show that the zeros of sampled-data systems resulting from rapid sampling of continuous-time systems preceded by a zero-order hold (ZOH) are the roots of the Euler– Frobenius polynomials. Using known properties of these polynomials, we prove two conjectures of Hagiwara and co-workers, the first of which concerns the simplicity, negative realness and interlacing properties of t...

Spectrum Properties of the Koopman and Frobenius-Perron Operators