Hurwitz polynomial
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A Hurwitz polynomial is a polynomial whose coefficients are positive real numbers and whose zeros are located in the left half-plane of the complex plane, that is, the real part of every zero is negative. One sometimes uses the term Hurwitz polynomial simply as a (real or complex) polynomial with all zeros in the left-half plane (i.e., a Hurwitz stable polynomial). These polynomials are named after Adolf Hurwitz.
A simple example of a Hurwitz polynomial is the following:
- <math>x^2 + 2x + 1<math>
The only real solution is −1, as it factors to:
- <math>(x+1)^2.<math>Template:Math-stub