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Man Ho Ling - One of the best experts on this subject based on the ideXlab platform.

  • multiple stress model for one shot device testing data under exponential distribution
    IEEE Transactions on Reliability, 2012
    Co-Authors: N Balakrishnan, Man Ho Ling
    Abstract:

    Left- and right-censored life time data arise naturally in one-shot device testing. An experimenter is often interested in identifying the effects of several stress variables on the lifetime of a device, and furthermore multiple-stress experiments controlling simultaneously several variables, result in reducing the experimental time as well as the cost of the experiment. Here, we present an expectation-maximization (EM) algorithm for developing inference on the reliability at a specific time, as well as the mean lifetime of the device based on one-shot device testing data under the exponential distribution when there are multiple stress factors. We use the log-linear link function for this purpose. Unlike in the typical EM algorithm, it is not necessary to obtain maximum likelihood estimates (MLEs) of the parameters at each Step of the iteration. By using the one-Step Newton-Raphson method, we observe that the convergence occurs quickly. We also use the jackknife technique to reduce the bias of the estimate obtained from the EM algorithm. In addition, we discuss the construction of confidence intervals for some reliability characteristics by using the asymptotic properties of the MLEs based on the observed Fisher information matrix, as well as by the jackknife technique, the parametric bootstrap methods, and a transformation technique. Finally, we present an example to illustrate all the inferential methods developed here.

  • multiple stress model for one shot device testing data under exponential distribution
    IEEE Transactions on Reliability, 2012
    Co-Authors: N Balakrishnan, Man Ho Ling
    Abstract:

    Left- and right-censored life time data arise naturally in one-shot device testing. An experimenter is often interested in identifying the effects of several stress variables on the lifetime of a device, and furthermore multiple-stress experiments controlling simultaneously several variables, result in reducing the experimental time as well as the cost of the experiment. Here, we present an expectation-maximization (EM) algorithm for developing inference on the reliability at a specific time, as well as the mean lifetime of the device based on one-shot device testing data under the exponential distribution when there are multiple stress factors. We use the log-linear link function for this purpose. Unlike in the typical EM algorithm, it is not necessary to obtain maximum likelihood estimates (MLEs) of the parameters at each Step of the iteration. By using the one-Step Newton-Raphson method, we observe that the convergence occurs quickly. We also use the jackknife technique to reduce the bias of the estimate obtained from the EM algorithm. In addition, we discuss the construction of confidence intervals for some reliability characteristics by using the asymptotic properties of the MLEs based on the observed Fisher information matrix, as well as by the jackknife technique, the parametric bootstrap methods, and a transformation technique. Finally, we present an example to illustrate all the inferential methods developed here.

Ioannis K Argyros - One of the best experts on this subject based on the ideXlab platform.

  • on the local convergence of two Step Newton type method in banach spaces under generalized lipschitz conditions
    Mathematics, 2021
    Co-Authors: Akanksha Saxena, Ioannis K Argyros, J P Jaiswal, Christopher I Argyros, Kamal R Pardasani
    Abstract:

    The motive of this paper is to discuss the local convergence of a two-Step Newton-type method of convergence rate three for solving nonlinear equations in Banach spaces. It is assumed that the first order derivative of nonlinear operator satisfies the generalized Lipschitz i.e., L-average condition. Also, some results on convergence of the same method in Banach spaces are established under the assumption that the derivative of the operators satisfies the radius or center Lipschitz condition with a weak L-average particularly it is assumed that L is positive integrable function but not necessarily non-decreasing. Our new idea gives a tighter convergence analysis without new conditions. The proposed technique is useful in expanding the applicability of iterative methods. Useful examples justify the theoretical conclusions.

  • on the local and semilocal convergence of a parameterized multi Step Newton method
    Journal of Computational and Applied Mathematics, 2020
    Co-Authors: Sergio Amat, Ioannis K Argyros, Sonia Busquier, M A Hernandezveron, Dionisio F Yanez
    Abstract:

    Abstract This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. We perform a convergence study and an analysis of the efficiency. This analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation. The method can be applied to many type of problems, including the discretization of ordinary differential equations, integral equations, integro-differential equations or partial differential equations. Moreover, multi-Step iterative methods are computationally attractive.

  • weak semilocal convergence conditions for a two Step Newton method in banach space
    Fundamental Journal of Mathematics and Applications, 2018
    Co-Authors: Ioannis K Argyros, Santhosh George
    Abstract:

    We present new sufficient convergence conditions for a two Step Newton method (TSNM) to solve nonlinear equations in a Banach space setting. The new conditions depend on the center-Lipschitz constant instead of the Lipschitz constant. This way the applicability of (TSNM) is expanded in cases not covered before. Numerical examples are also provided in this study.

  • predetermining the number of periodic Steps in multi Step Newton like methods for solving equations and systems of equations
    Applied Mathematics and Computation, 2018
    Co-Authors: Ioannis K Argyros, ştefan Măruster
    Abstract:

    Abstract The goal of this paper is to predetermine the Steps m after which the first derivative is re–evaluated for multi-Step Newton-type method used to approximate solutions of equations.

  • local convergence of a relaxed two Step Newton like method with applications
    Journal of Mathematical Chemistry, 2017
    Co-Authors: Ioannis K Argyros, Á. Alberto Magreñán, Lara Orcos, Juan Antonio Sicilia
    Abstract:

    We present a local convergence analysis for a relaxed two-Step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Frechet derivative and on the center divided-difference of order one are used. In earlier studies such as Amat et al. (Numer Linear Algebra Appl 17:639–653, 2010, Appl Math Lett 25(12):2209–2217, 2012, Appl Math Comput 219(24):11341–11347, 2013, Appl Math Comput 219(15):7954–7963, 2013, Reducing Chaos and bifurcations in Newton-type methods. Abstract and applied analysis. Hindawi Publishing Corporation, Cairo, 2013) these methods are analyzed under hypotheses up to the second Frechet derivative and divided differences of order one. Numerical examples are also provided in this work.

Frederic Barlat - One of the best experts on this subject based on the ideXlab platform.

  • stress integration schemes for novel homogeneous anisotropic hardening model
    Computer Methods in Applied Mechanics and Engineering, 2012
    Co-Authors: Frederic Barlat
    Abstract:

    Abstract Numerical formulations and implementation of stress integration algorithms in the elasto-plastic finite element method are provided for the homogeneous yield function-based anisotropic hardening (HAH) model. This model is able to describe complex material behavior under non-monotonic loading conditions. Two numerical algorithms based on the semi-explicit and fully implicit schemes are compared in terms of accuracy. To efficiently treat the yield locus distortion when the strain path changes, a multi-Step Newton–Raphson method is proposed to calculate the first and second derivatives of the HAH yield surface. For the validation of the developed numerical algorithms, the r -value anisotropy is compared for the conventional yield model with classical isotropic hardening and for the HAH model. Moreover, detailed error analysis is presented using iso-error maps. The results show that the fully implicit stress integration algorithm based on the closet point projection method leads to better accuracy in general. However, the semi-explicit algorithm also provides comparable accuracy if an appropriate time increment is chosen. Furthermore in spite of the yield surface distortion, the developed numerical algorithms can successfully update stress with the equivalent level of the error for the conventional yield model.

  • finite element modeling using homogeneous anisotropic hardening and application to spring back prediction
    International Journal of Plasticity, 2012
    Co-Authors: Frederic Barlat
    Abstract:

    Abstract A finite element (FE) implementation of the recently proposed constitutive model (Homogeneous yield function-based anisotropic hardening model or HAH; doi:10.1016/j.ij-plas.2011.03.003 in International Journal of Plasticity) that describes the plastic behavior of materials subjected to multiple strain path changes was developed. A complete formulation based on the return-mapping algorithm for the yield function was proposed. In particular, a multi-Step Newton–Raphson method was introduced to calculate the gradient of the HAH model for the stress integration procedure. In addition to the numerical aspects, the theoretical proofs of the stability and convexity of the HAH model were discussed. For verification purpose, simple finite element simulations were conducted and the results were compared to those obtained from various constitutive models. Finally, mechanical characterization and U-draw bend experiments were performed on DP590 and TRIP590 steel sheet samples. The springback was quantified using the parameters defined at the NUMISHEET (1993) benchmark. Simulations of the 2D draw-bend test were performed with the FE code and the HAH constitutive description for DP590 and TRIP590 steel sheet samples. All the predicted springback values for these materials were in good agreement with experimental data.

N Balakrishnan - One of the best experts on this subject based on the ideXlab platform.

  • multiple stress model for one shot device testing data under exponential distribution
    IEEE Transactions on Reliability, 2012
    Co-Authors: N Balakrishnan, Man Ho Ling
    Abstract:

    Left- and right-censored life time data arise naturally in one-shot device testing. An experimenter is often interested in identifying the effects of several stress variables on the lifetime of a device, and furthermore multiple-stress experiments controlling simultaneously several variables, result in reducing the experimental time as well as the cost of the experiment. Here, we present an expectation-maximization (EM) algorithm for developing inference on the reliability at a specific time, as well as the mean lifetime of the device based on one-shot device testing data under the exponential distribution when there are multiple stress factors. We use the log-linear link function for this purpose. Unlike in the typical EM algorithm, it is not necessary to obtain maximum likelihood estimates (MLEs) of the parameters at each Step of the iteration. By using the one-Step Newton-Raphson method, we observe that the convergence occurs quickly. We also use the jackknife technique to reduce the bias of the estimate obtained from the EM algorithm. In addition, we discuss the construction of confidence intervals for some reliability characteristics by using the asymptotic properties of the MLEs based on the observed Fisher information matrix, as well as by the jackknife technique, the parametric bootstrap methods, and a transformation technique. Finally, we present an example to illustrate all the inferential methods developed here.

  • multiple stress model for one shot device testing data under exponential distribution
    IEEE Transactions on Reliability, 2012
    Co-Authors: N Balakrishnan, Man Ho Ling
    Abstract:

    Left- and right-censored life time data arise naturally in one-shot device testing. An experimenter is often interested in identifying the effects of several stress variables on the lifetime of a device, and furthermore multiple-stress experiments controlling simultaneously several variables, result in reducing the experimental time as well as the cost of the experiment. Here, we present an expectation-maximization (EM) algorithm for developing inference on the reliability at a specific time, as well as the mean lifetime of the device based on one-shot device testing data under the exponential distribution when there are multiple stress factors. We use the log-linear link function for this purpose. Unlike in the typical EM algorithm, it is not necessary to obtain maximum likelihood estimates (MLEs) of the parameters at each Step of the iteration. By using the one-Step Newton-Raphson method, we observe that the convergence occurs quickly. We also use the jackknife technique to reduce the bias of the estimate obtained from the EM algorithm. In addition, we discuss the construction of confidence intervals for some reliability characteristics by using the asymptotic properties of the MLEs based on the observed Fisher information matrix, as well as by the jackknife technique, the parametric bootstrap methods, and a transformation technique. Finally, we present an example to illustrate all the inferential methods developed here.

Á. Alberto Magreñán - One of the best experts on this subject based on the ideXlab platform.

  • local convergence of a relaxed two Step Newton like method with applications
    Journal of Mathematical Chemistry, 2017
    Co-Authors: Ioannis K Argyros, Á. Alberto Magreñán, Lara Orcos, Juan Antonio Sicilia
    Abstract:

    We present a local convergence analysis for a relaxed two-Step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Frechet derivative and on the center divided-difference of order one are used. In earlier studies such as Amat et al. (Numer Linear Algebra Appl 17:639–653, 2010, Appl Math Lett 25(12):2209–2217, 2012, Appl Math Comput 219(24):11341–11347, 2013, Appl Math Comput 219(15):7954–7963, 2013, Reducing Chaos and bifurcations in Newton-type methods. Abstract and applied analysis. Hindawi Publishing Corporation, Cairo, 2013) these methods are analyzed under hypotheses up to the second Frechet derivative and divided differences of order one. Numerical examples are also provided in this work.

  • Local Convergence and the Dynamics of a Two-Step Newton-Like Method
    International Journal of Bifurcation and Chaos, 2016
    Co-Authors: Ioannis K Argyros, Á. Alberto Magreñán
    Abstract:

    We present the local convergence analysis and the study of the dynamics of a two-Step Newton-like method in order to approximate a locally unique solution of multiplicity one of a nonlinear equation.

  • On the election of the damped parameter of a two-Step relaxed Newton-type method
    Nonlinear Dynamics, 2016
    Co-Authors: Sergio Amat, Sonia Busquier, Concepción Bermúdez, Á. Alberto Magreñán
    Abstract:

    In this paper, we are interested to justified two typical hypotheses that appear in the convergence analysis, $$|\lambda |\le 2$$ | λ | ≤ 2 and $$z_0$$ z 0 sufficient close to $$z^*$$ z ∗ . In order to proof these ideas, the dynamics of a damped two-Step Newton-type method for solving nonlinear equations and systems is presented. We present the parameter space for values of the damping factor in the complex plane, focusing our attention in such values for which the fixed points related to the roots are attracting. Moreover, we study the stability of the strange fixed points, showing that there exists attracting cycles and chaotical behavior for some choices of the damping factor.