Natalia Romero

In this work, we analyze a strategy for solving symmetric algebraic Riccati equation based on the use of efficient high-order iterative scheme. This iterative scheme is more efficient than Newton’s method. Then, we propose two iterative two-stage predictor–corrector schemes using an iterative scheme with good accessibility as the predictor iteration and a high-order iterative scheme as the corrector iteration. The iterative schemes constructed turn out to be competitive compared to the commonly used Newton’s method. The efficiency of these methods is illustrated by a numerical example.

Outline we provoke a discussion based on our experience of working in brazil and ecuador, where we have a unit focused on the social and environmental determinants of health inequalities: Health inequalities are in large part attributable to the social determinants of health – the conditions...

In this paper we consider the Catalan triangle numbers ( B n , k ) n ≥ 1 , 1 ≤ k ≤ n and ( A n , k ) n ≥ 1 , 1 ≤ k ≤ n + 1 to define powers of Catalan generating function C ( T ) where T is a linear and bounded operator on a Banach space X . When the operator 4 T is of power-bounded operator, the Catalan generating function is given by the Taylor series C ( T ) : = ∑ n = 0 ∞ C n T n , where c = ( C n ) n ≥ 0 is the Catalan sequence. Note that the operator C ( T ) is a solution of the quadratic equation T Y 2 − Y + I = 0 . We obtain new formulae which involves Catalan triangle numbers ( B n , k ) n ≥ 1 , 1 ≤ k ≤ n and ( A n , k ) n ≥ 1 , 1 ≤ k ≤ n + 1 . As element in the Banach algebra ℓ 1 ( N 0 , 1 4 n ) , we describe the spectrum of c ∗ j for j ≥1, and the expression of c −∗ j in terms of Catalan polynomials. In the last section, we give some particular examples to illustrate our results and some ideas to continue this research in the future.

In this work, we focus on analyzing the location and separation of the solutions of the simplest quadratic matrix equation. For this, we use the qualitative properties that we can deduce of the study of the convergence of iterative processes. This study allow us to determine domains of existence and uniqueness of solutions, and therefore to locate and separate the solutions. Another goal is to approximate a solution of the quadratic matrix equation. For this, we consider iterative processes of fixed point type. So, analyzing the convergence of these iterative processes of fixed point type, we locate, separate and approximate solutions of quadratic matrix equations.

In this paper, we study the simplest quadratic matrix equation: . We transform this equation into an equivalent fixed‐point equation, and based on it, we construct the Krasnoselskij method. From this transformation, we can obtain iterative schemes more accurate than the successive approximation method. Moreover, under suitable conditions, we establish different results for the existence and localization of a solution for this equation with the Krasnoselskij method. Finally, we see numerically that the predictor–corrector iterative scheme, with the Krasnoselskij method as a predictor and the Newton method as corrector method, can improve the numerical application of the Newton method when approximating a solution of the quadratic matrix equation.