Matrix polynomials play an important role in the theory of matrix differential equations. We develop a fixed point method to compute solutions of matrix polynomials equations, where the matricial elements of the matrix polynomial are considered separately as complex polynomials. Numerical examples illustrate the method presented.
We prove that any linear ordinary differential operator with complex-valued coefficients continuous in an interval I can be factored into a product of first-order operators globally defined on I. This generalizes a theorem of Mammana for the case of real-valued coefficients.
Let f be a C1 function defined over Rn and definable in a given o-minimal structure M expanding the real field. We prove here a gradient-like inequality at infinity in a neighborhood of an asymptotic critical value c. When f is C2 we use this inequality to discuss the trivialization by the gradient flow of f in a neighborhood of a regular asymptotic critical level.
A generalized Gronwall-like inequality is established and applied in obtaining a right saturated solution for a class of differential equations and in estimating the solution of an evolution equation for the so called hidden variables.
Shifting a numerically given function we obtain a fundamental matrix of the linear differential system with a constant matrix . Using the fundamental matrix we calculate , calculating the eigenvalues of we obtain and using the least square method we determine .