Home / Journals / CMES / Vol.76, No.2, 2011
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  • Open Access

    ARTICLE

    Dynamical Newton-Like Methods for Solving Ill-Conditioned Systems of Nonlinear Equations with Applications to Boundary Value Problems

    Cheng-Yu Ku1,2,3,Weichung Yeih1,2, Chein-Shan Liu4
    CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 83-108, 2011, DOI:10.3970/cmes.2011.076.083
    Abstract In this paper, a general dynamical method based on the construction of a scalar homotopy function to transform a vector function of Non-Linear Algebraic Equations (NAEs) into a time-dependent scalar function by introducing a fictitious time-like variable is proposed. With the introduction of a transformation matrix, the proposed general dynamical method can be transformed into several dynamical Newton-like methods including the Dynamical Newton Method (DNM), the Dynamical Jacobian-Inverse Free Method (DJIFM), and the Manifold-Based Exponentially Convergent Algorithm (MBECA). From the general dynamical method, we can also derive the conventional Newton method using a certain fictitious time-like function. The formulation presented… More >

  • Open Access

    ARTICLE

    A Dynamical Tikhonov Regularization Method for Solving Nonlinear Ill-Posed Problems

    Chein-Shan Liu1, Chung-Lun Kuo2
    CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 109-132, 2011, DOI:10.3970/cmes.2011.076.109
    Abstract The Tikhonov method is a famous technique for regularizing ill-posed systems. In this theory a regularization parameter α needs to be determined. Based-on an invariant-manifold defined in the space of (x,t) and from the Tikhonov minimization functional, we can derive an optimal vector driven system of nonlinear ordinary differential equations (ODEs). In the Optimal Vector Driven Algorithm (OVDA), the optimal regularization parameter αk is presented in the iterative solution of x, which means that a dynamical Tikhonov regularization method is involved in the solution of nonlinear ill-posed problem. The OVDA is an extension of the Landweber-Scherzer iterative algorithm. Numerical examples… More >

  • Open Access

    ARTICLE

    Rebirth of a Discipline: "Knowledge Engineering"

    Ziya Aktas1, Semih Cetin2
    CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.2, pp. 133-162, 2011, DOI:10.3970/cmes.2011.076.133
    Abstract The knowledge society has been developed and shaped by amazing improvements during the last two decades. On that development and improvement, social sciences such as psychology or anthropology have also had significant impact as much as real sciences like medicine or engineering, in particular, Information Technology or Information and Communications Technology. The new trends and explosion of knowledge due to Internet and Web technologies have radically changed the way we structure business and its main building block, i.e. "knowledge". Though information/knowledge system development efforts have been regarded formerly as mere information technology activities, now we have been experiencing alternative ways… More >

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