Least Roots of Equations

Least Squares Solutions of Inconsistent Fuzzy Linear Matrix Equations

The Stationary - NonStationary Process and The Variable Roots Difference Equations

Stochastic, processes can be stationary or nonstationary. They depend on the magnitude of shocks. In other words, in an auto regressive model of order one, the estimated coefficient is not constant. Another finding of this paper is the relation between estimated coefficients and residuals. We also develop a catastrophe and chaos theory for change of roots from stationary to a nonstationary one ...

Solving algebraic equations in roots of unity

This paper is devoted to finding solutions of polynomial equations in roots of unity. It was conjectured by S. Lang and proved by M. Laurent that all such solutions can be described in terms of a finite number of parametric families called maximal torsion cosets. We obtain new explicit upper bounds for the number of maximal torsion cosets on an algebraic subvariety of the complex algebraic n-to...

On Enclosing Simple Roots of Nonlinear Equations

In this paper we present two efficient algorithms for enclosing a simple root of the nonlinear equation f(x) = 0 in the interval [a, b]. They improve recent methods of Alefeld and Potra by achieving higher efficiency indices and avoiding the solution of a quadratic equation per iteration. The efficiency indices of our methods are 1.5537... and 1.618... , respectively. We show that our second me...

Completing Bethe’s equations at roots of unity

In a previous paper we demonstrated that Bethe’s equations are not sufficient to specify the eigenvectors of the XXZ model at roots of unity for states where the Hamiltonian has degenerate eigenvalues. We here find the equations which will complete the specification of the eigenvectors in these degenerate cases and present evidence that the sl2 loop algebra symmetry is sufficiently powerful to ...