5,654 research outputs found
New Structured Matrix Methods for Real and Complex Polynomial Root-finding
We combine the known methods for univariate polynomial root-finding and for
computations in the Frobenius matrix algebra with our novel techniques to
advance numerical solution of a univariate polynomial equation, and in
particular numerical approximation of the real roots of a polynomial. Our
analysis and experiments show efficiency of the resulting algorithms.Comment: 18 page
Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
We present a numerical approach which allows the solving of Bethe equations
whose solutions define the eigenstates of Gaudin models. By focusing on a new
set of variables, the canceling divergences which occur for certain values of
the coupling strength no longer appear explicitly. The problem is thus reduced
to a set of quadratic algebraic equations. The required inverse transformation
can then be realized using only linear operations and a standard polynomial
root finding algorithm. The method is applied to Richardson's fermionic pairing
model, the central spin model and generalized Dicke model.Comment: 10 pages, 3 figures, published versio
- …