No polynomial algorithms are known for finding the coefficients of the characteristic polynomial and characteristic equation of a matrix in max-algebra. The following are proved: (1) The task of finding the max-algebraic characteristic polynomial for permutation matrices encoded using the lengths of their constituent cycles is IVP-complete. (2) The task of finding the lowest order finite term o...

Both linear time-invariant (LTI) and linear time-varying (LTV) systems are addressed. They are placed in a unified conceptual framework. The characteristic equation for each subclass is formulated as a Riccati equation. Where LTI-systems lead to algebraic Riccati equations, the LTV-case generalizes this result to differential Riccati equations.

Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper and monic (or regular) triangular set is given. An improved zero decomposition algorithm which can be used to reduce the zero set of an equation system in ge...

This paper introduces a mesh generating algorithm for solving the traffic flow equation as a conservation law equation. The idea behind the new method is to use the characteristic curves and moving non-oscillatory finite volume method. In addition, when characteristic curves intersect, the proposed scheme uses shock speed equation in order to improve computational efficiency. We also compare th...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...