Instituto de Matemática

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Browsing Instituto de Matemática by Author "Elaine Segura"

Now showing 1 - 5 of 5
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    Behind Jarratt’s Steps: Is Jarratt’s Scheme the Best Version of Itself
    (2023-06-15) Elaine Segura
    In this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt’s method is the most stable among all the elements of the family. We deduce that classical Jarratt’s scheme is not the only stable element of the family. We also obtain information about the members of the class with chaotical behavior. Some numerical results are presented for confirming the convergence and stability results.
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    Behind Jarratt’s Steps: Is Jarratt’s Scheme the best version of itself?
    (2023-06-15) Elaine Segura
    In this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt’s method is the most stable among all the elements of the family. We deduce that classical Jarratt’s scheme is not the only stable element of the family. We also obtain information about the members of the class with chaotical behavior. Some numerical results are presented for confirming the convergence and stability results.
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    Diagonal entries of the combined matrix of sign regular matrices of order three
    (2021-01-16) Elaine Segura; Máximo Santana
    El estudio de las entradas diagonales de la matriz combinada de una matriz no singular A ha sido considerado por diferentes autores para las clases de M—matrices, matrices definidas positivas y matrices totalmente positivas (negativas). Este problema parece ser difícil ya que los resultados se han hecho sólo para matrices de orden tres. En este trabajo, continuamos dando la caracterización de las entradas diagonales de la matriz combinada del resto de matrices regulares de signos. Por lo tanto, el problema se cierra para todas las matrices regulares de signos posibles de orden tres.
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    Inverse matrix estimations by interative methods with weight functions and their stability analysis
    (2024-09) Elaine Segura
    "In this paper, we construct a parametric family of iterative methods to compute the inverse of a nonsingular matrix. This class is free of inverse operators. We prove the third-order of convergence under some conditions involving the parameter of the family. Moreover, a dynamical analysis is made for the first time to a matrix iterative method, finding intervals of stability, that include but are wider than those found in the convergence analysis. Numerical tests on large random matrices confirm the results found. "
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    New iterative procedures for approximating different types of inverse matrix: convergence and stability,
    (2025-01-25) Elaine Segura
    In this paper, we propose a new parametric family of iterative schemes to compute the inverse of a complex nonsingular matrix. It is shown that the members of this family have at least a fourth order of convergence. A particular element of the class is extended to approximate the Moore–Penrose inverse of rectangular complex matrices, keeping the convergence order. A dynamic analysis is performed to obtain a parameter domain in which stability is assured and to detect which members of the proposed family have good stability properties and which have chaotic behavior. Some numerical examples, with matrices of different sizes, are tested to confirm the theoretical and dynamical results.