The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform

Ryozo Nagamune - One of the best experts on this subject based on the ideXlab platform.

D. K. Gupta - One of the best experts on this subject based on the ideXlab platform.

  • A Continuation Method AND ITS CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS IN BANACH SPACES
    International Journal of Computational Methods, 2013
    Co-Authors: M. Prashanth, D. K. Gupta
    Abstract:

    A Continuation Method is a parameter based iterative Method establishing a continuous connection between two given functions/operators and used for solving nonlinear equations in Banach spaces. The semilocal convergence of a Continuation Method combining Chebyshev's Method and Convex acceleration of Newton's Method for solving nonlinear equations in Banach spaces is established in [J. A. Ezquerro, J. M. Gutiérrez and M. A. Hernández [1997] J. Appl. Math. Comput.85: 181–199] using majorizing sequences under the assumption that the second Frechet derivative satisfies the Lipschitz continuity condition. The aim of this paper is to use recurrence relations instead of majorizing sequences to establish the convergence analysis of such a Method. This leads to a simpler approach with improved results. An existence–uniqueness theorem is given. Also, a closed form of error bounds is derived in terms of a real parameter α ∈ [0, 1]. Four numerical examples are worked out to demonstrate the efficacy of our convergence analysis. On comparing the existence and uniqueness region and error bounds for the solution obtained by our analysis with those obtained by using majorizing sequences, it is found that our analysis gives better results in three examples, whereas in one example it gives the same results. Further, we have observed that for particular values of the α, our analysis reduces to those for Chebyshev's Method (α = 0) and Convex acceleration of Newton's Method (α = 1) respectively with improved results.

  • A Continuation Method AND ITS CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS IN BANACH SPACES
    International Journal of Computational Methods, 2013
    Co-Authors: M. Prashanth, D. K. Gupta
    Abstract:

    A Continuation Method is a parameter based iterative Method establishing a continuous connection between two given functions/operators and used for solving nonlinear equations in Banach spaces. The semilocal convergence of a Continuation Method combining Chebyshev's Method and Convex acceleration of Newton's Method for solving nonlinear equations in Banach spaces is established in [J. A. Ezquerro, J. M. Gutierrez and M. A. Hernandez [1997] J. Appl. Math. Comput.85: 181–199] using majorizing sequences under the assumption that the second Frechet derivative satisfies the Lipschitz continuity condition. The aim of this paper is to use recurrence relations instead of majorizing sequences to establish the convergence analysis of such a Method. This leads to a simpler approach with improved results. An existence–uniqueness theorem is given. Also, a closed form of error bounds is derived in terms of a real parameter α ∈ [0, 1]. Four numerical examples are worked out to demonstrate the efficacy of our convergence analysis. On comparing the existence and uniqueness region and error bounds for the solution obtained by our analysis with those obtained by using majorizing sequences, it is found that our analysis gives better results in three examples, whereas in one example it gives the same results. Further, we have observed that for particular values of the α, our analysis reduces to those for Chebyshev's Method (α = 0) and Convex acceleration of Newton's Method (α = 1) respectively with improved results.

  • Convergence of a Continuation Method under Lipschitz continuous derivative in Banach spaces
    Journal of Applied Mathematics and Computing, 2011
    Co-Authors: M. Prashanth, D. K. Gupta
    Abstract:

    The aim of this paper is to use recurrence relations instead of majorizing sequences to establish the semilocal convergence of a Continuation Method combining Chebyshev Method and Convex acceleration of Newton’s Method for solving nonlinear equations in Banach spaces under the assumption that the first Frechet derivative satisfies the Lipschitz continuity condition. An existence-uniqueness theorem is given. Also, a closed form of error bounds is derived in terms of a real parameter α∈[0,1]. Two numerical examples are worked out to demonstrate the efficacy of our convergence analysis. On comparing the existence and uniqueness regions for the solution obtained by our analysis with those obtained by using majorizing sequences, it is found that our analysis gives better results in both the examples. Further, we observed that for particular values of α, our analysis reduces to those for Chebyshev Method (α=0) and Convex acceleration of Newton’s Method (α=1) respectively with improved results.

Bin Wang - One of the best experts on this subject based on the ideXlab platform.

  • holomorphic embedding based Continuation Method for identifying multiple power flow solutions
    IEEE Access, 2019
    Co-Authors: Bin Wang
    Abstract:

    In this paper, we propose an efficient Continuation Method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The holomorphicity, which provides global information of the curve at any regular point, enables large step sizes in the path-following procedure such that non-singular curve segments can be traversed with very few steps. When approaching singular points, we switch to the traditional predictor-corrector routine to pass through them and switch back afterward to the holomorphic embedding routine. We also propose a warm starter when switching to the predictor-corrector routine, i.e., a large initial step size based on the poles of the Pade approximation of the derived holomorphic function, since these poles reveal the locations of singularities on the curve. The numerical analysis and experiments on many standard IEEE test cases are presented, along with the comparison to the full predictor-corrector routine, confirming the efficiency of the Method.

A C Z De Souza - One of the best experts on this subject based on the ideXlab platform.

  • tracing pv and qv curves with the help of a cric Continuation Method
    IEEE Transactions on Power Systems, 2006
    Co-Authors: Fritz Walter Mohn, A C Z De Souza
    Abstract:

    This paper investigates the use of the constraint reactive implicit coupling (CRIC) Method for the engine of a Continuation power flow program. Full Newton Continuation power flow Methods are robust and accurate but are computationally expensive. Fast decoupled Methods provide accurate results and require less computational time, but their performance worsens at heavy loading conditions, where the system active/reactive power decoupling characteristics are lost. This paper makes use of the CRIC Method, which preserves the decoupled power flow solution structure but better models the active/reactive coupling. Effective stopping criteria are proposed for the Continuation Method, which helps to speed up computation. Such stopping criteria are also applied for tracing QV curves for some practical Brazilian power systems, with all operating limits considered

M. Prashanth - One of the best experts on this subject based on the ideXlab platform.

  • A Continuation Method AND ITS CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS IN BANACH SPACES
    International Journal of Computational Methods, 2013
    Co-Authors: M. Prashanth, D. K. Gupta
    Abstract:

    A Continuation Method is a parameter based iterative Method establishing a continuous connection between two given functions/operators and used for solving nonlinear equations in Banach spaces. The semilocal convergence of a Continuation Method combining Chebyshev's Method and Convex acceleration of Newton's Method for solving nonlinear equations in Banach spaces is established in [J. A. Ezquerro, J. M. Gutiérrez and M. A. Hernández [1997] J. Appl. Math. Comput.85: 181–199] using majorizing sequences under the assumption that the second Frechet derivative satisfies the Lipschitz continuity condition. The aim of this paper is to use recurrence relations instead of majorizing sequences to establish the convergence analysis of such a Method. This leads to a simpler approach with improved results. An existence–uniqueness theorem is given. Also, a closed form of error bounds is derived in terms of a real parameter α ∈ [0, 1]. Four numerical examples are worked out to demonstrate the efficacy of our convergence analysis. On comparing the existence and uniqueness region and error bounds for the solution obtained by our analysis with those obtained by using majorizing sequences, it is found that our analysis gives better results in three examples, whereas in one example it gives the same results. Further, we have observed that for particular values of the α, our analysis reduces to those for Chebyshev's Method (α = 0) and Convex acceleration of Newton's Method (α = 1) respectively with improved results.

  • A Continuation Method AND ITS CONVERGENCE FOR SOLVING NONLINEAR EQUATIONS IN BANACH SPACES
    International Journal of Computational Methods, 2013
    Co-Authors: M. Prashanth, D. K. Gupta
    Abstract:

    A Continuation Method is a parameter based iterative Method establishing a continuous connection between two given functions/operators and used for solving nonlinear equations in Banach spaces. The semilocal convergence of a Continuation Method combining Chebyshev's Method and Convex acceleration of Newton's Method for solving nonlinear equations in Banach spaces is established in [J. A. Ezquerro, J. M. Gutierrez and M. A. Hernandez [1997] J. Appl. Math. Comput.85: 181–199] using majorizing sequences under the assumption that the second Frechet derivative satisfies the Lipschitz continuity condition. The aim of this paper is to use recurrence relations instead of majorizing sequences to establish the convergence analysis of such a Method. This leads to a simpler approach with improved results. An existence–uniqueness theorem is given. Also, a closed form of error bounds is derived in terms of a real parameter α ∈ [0, 1]. Four numerical examples are worked out to demonstrate the efficacy of our convergence analysis. On comparing the existence and uniqueness region and error bounds for the solution obtained by our analysis with those obtained by using majorizing sequences, it is found that our analysis gives better results in three examples, whereas in one example it gives the same results. Further, we have observed that for particular values of the α, our analysis reduces to those for Chebyshev's Method (α = 0) and Convex acceleration of Newton's Method (α = 1) respectively with improved results.

  • Convergence of a Continuation Method under Lipschitz continuous derivative in Banach spaces
    Journal of Applied Mathematics and Computing, 2011
    Co-Authors: M. Prashanth, D. K. Gupta
    Abstract:

    The aim of this paper is to use recurrence relations instead of majorizing sequences to establish the semilocal convergence of a Continuation Method combining Chebyshev Method and Convex acceleration of Newton’s Method for solving nonlinear equations in Banach spaces under the assumption that the first Frechet derivative satisfies the Lipschitz continuity condition. An existence-uniqueness theorem is given. Also, a closed form of error bounds is derived in terms of a real parameter α∈[0,1]. Two numerical examples are worked out to demonstrate the efficacy of our convergence analysis. On comparing the existence and uniqueness regions for the solution obtained by our analysis with those obtained by using majorizing sequences, it is found that our analysis gives better results in both the examples. Further, we observed that for particular values of α, our analysis reduces to those for Chebyshev Method (α=0) and Convex acceleration of Newton’s Method (α=1) respectively with improved results.