The Experts below are selected from a list of 5649 Experts worldwide ranked by ideXlab platform
O. I. Hryhorchak - One of the best experts on this subject based on the ideXlab platform.
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Analytical representation of an Iterative Formula for a quantum wave impedance determination in a case of a piecewise constant potential.
arXiv: Quantum Physics, 2020Co-Authors: O. I. HryhorchakAbstract:An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known Iterative method of a quantum wave impedance determination. The expression for a transmission probability as a function of a particle energy for an arbitrary cascad of constant potentials was obtained. The application of obtained results was illustrated on a system of double-well/barrier structures.
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Quantum wave impedance calculation for an arbitrary piesewise constant potential
arXiv: Quantum Physics, 2020Co-Authors: O. I. HryhorchakAbstract:The method of a determination of a quantum wave impedance for an arbitrary piecewise constant potential was developed. On the base of this method both the well-known Iterative Formula \cite{Khondker_Khan_Anwar:1988} and alternative ways for a quantum wave impedance calculation were derived. A scattering and a bound state case were considered. The general form of a wave function of bound states for an arbitrary piesewise constant potential was obtained as well as transmission and reflection coefficients in a scattering case. The applying of method was demonstarted on the system of double well/barrier.
Behrooz Keshtegar - One of the best experts on this subject based on the ideXlab platform.
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three term conjugate approach for structural reliability analysis
Applied Mathematical Modelling, 2019Co-Authors: Behrooz KeshtegarAbstract:Abstract In this paper, a nonlinear conjugate structural first-order reliability method is proposed using three-term conjugate discrete map-based sensitivity analysis to enhance convergence properties as stable results and efficient computational burden of nonlinear reliability problems. The concept of finite-step length strategy is incorporated into this method to enhance the stability of the Iterative Formula for highly nonlinear limit state function, while three-term conjugate search direction combining with a finite-step size is utilized to enhance the efficiency of the sensitivity vector in the proposed Iterative reliability Formula. The proposed three-term discrete conjugate search direction is developed based on the sufficient descent condition to provide the stable results, theoretically. The efficiency and robustness of the proposed three-term conjugate Formula are investigated through several nonlinear/ complex structural examples and are compared with several modified existing Iterative Formulas. Comparative results illustrate that the three-term conjugate-based finite step length Formula provides superior efficiency and robustness than other studied methods.
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enriched self adjusted performance measure approach for reliability based design optimization of complex engineering problems
Applied Mathematical Modelling, 2018Co-Authors: Behrooz KeshtegarAbstract:Abstract For reliability-based design optimization (RBDO) of practical structural/mechanical problems under highly nonlinear constraints, it is an important characteristic of the performance measure approach (PMA) to show robustness and high convergence rate. In this study, self-adjusted mean value is used in the PMA Iterative Formula to improve the robustness and efficiency of the RBDO-based PMA for nonlinear engineering problems based on dynamic search direction. A novel merit function is applied to adjust the modified search direction in the enriched self-adjusted mean value (ESMV) method, which can control the instability and value of the step size for highly nonlinear probabilistic constraints in RBDO problems. The convergence performance of the enriched self-adjusted PMA is illustrated using four nonlinear engineering problems. In particular, a complex engineering example of aircraft stiffened panel is used to compare the RBDO results of different reliability methods. The results demonstrate that the proposed self-adjusted steepest descent search direction can improve the computational efficiency and robustness of the PMA compared to existing modified reliability methods for nonlinear RBDO problems.
Ming Jiang - One of the best experts on this subject based on the ideXlab platform.
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Relaxation strategy for the Landweber method
Signal Processing, 2016Co-Authors: Guanghui Han, Ming JiangAbstract:The Landweber iteration is a general method for the solution of linear systems which is widely applied for image reconstructions. The convergence behavior of the Landweber iteration is of both theoretical and practical importance. By the representation of the Iterative Formula and the convergence results of the Landweber iteration, we derive the optimal relaxation method under the minimization of the spectral radius of the newly derived Iterative matrix. We also establish the Iterative relaxation strategy to accelerate the convergence for the Landweber iteration when only the biggest singular value is available. As an immediate result, we derive the corresponding results for Richardson's iteration for the symmetric nonnegative definite linear systems. Finally, numerical simulations are conducted to validate the theoretical results. The advantage of the proposed relaxation strategies is demonstrated by comparing with the existing strategies. HighlightsWe derive the optimal relaxation method.We establish the Iterative relaxation strategy to accelerate the convergence.We derive the corresponding results for Richardson's iteration.Numerical simulations are conducted to validate the theoretical results.
Lei Jiang - One of the best experts on this subject based on the ideXlab platform.
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a sequential approximate programming strategy for performance measure based probabilistic structural design optimization
Structural Safety, 2008Co-Authors: Gengdong Cheng, Lei JiangAbstract:Abstract The evaluation of probabilistic constraints in the probabilistic structural design optimization (PSDO) problem can be carried out using either the conventional reliability index approach (RIA) or the more recently proposed performance measure approach (PMA). The latter is sometimes regarded as more efficient and stable with less dependence on probabilistic distribution types of random variables. Herein we apply PMA to evaluate probabilistic constraints and solve the PSDO using the sequential approximate programming (SAP) strategy. The sequential linear programming (SLP) approach in structural optimization achieves optimum design by solving a sequence of sub-programming problems Iteratively. Each sub-programming consists of a linear objective subjected to a set of linear constraints, all based on approximation of the original objective and constraints at the current design. Implementing this approach to PSDO in a straightforward manner will require linear approximation of probabilistic performance measure and its sensitivities, thus implying large number of iterations and huge computational cost. In our new approach, rather than using the linear expansion of the probabilistic performance measure, we propose a Formulation for an approximate probabilistic performance measure and its linearization. Obtained based on optimality conditions in the vicinity of the minimum performance target point (MPTP), the approximate measure and its sensitivity enables efficient sub-programming step. We update MPTP simultaneously at each step using Iterative Formula from the advanced mean-value (AMV) method and apply it as the initial estimate for the next step. As the sub-programming steps are no longer the linear approximation of the original problem, this is essentially a sequential approximate programming (SAP) approach. Through the application of this method to the most relevant examples frequently cited in similar studies, we compare its efficiency to other existing approaches and illustrate the concurrent convergence of both optimization and probabilistic performance measure calculation.
Hiroshi Sugiura - One of the best experts on this subject based on the ideXlab platform.
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Estimating convergence regions of Schröder’s iteration Formula: how the Julia set shrinks to the Voronoi boundary
Numerical Algorithms, 2018Co-Authors: Tomohiro Suzuki, Hiroshi Sugiura, Takemitsu HasegawaAbstract:Schroder’s Iterative Formula of the second kind (S2 Formula) for finding zeros of a function f(z) is a generalization of Newton’s Formula to an arbitrary order m of convergence. For Iterative Formulae, convergence regions of initial values to zeros in the complex plane z are essential. From numerical experiments, it is suggested that as order m of the S2 Formula grows, the complicated fractal structure of the boundary of convergence regions gradually diminishes. We propose a method of estimating the convergence regions with the circles of Apollonius to verify this result for polynomials f(z) with simple zeros. We indeed show that as m grows, each region surrounded by the circles of Apollonius monotonically enlarges to the Voronoi cell of a zero of f(z). Numerical examples illustrate convergence regions for several values of m and some polynomials.
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A high-order Iterative Formula for simultaneous determination of zeros of
1991Co-Authors: Tetsuya Sakurai, Tatsuo Torii, Hiroshi SugiuraAbstract:464-01, Japan Sakurai, T., T. Torii and H. Sugiura, A high-order Iterative Formula for simultaneous determination of zeros of a polynomial, Journal of Computational and Applied Mathematics 38 (1991) 387-397. We propose a hybrid method to determine all the zeros of a polynomial, simultaneously, by combining the single-root method and the simultaneous one. The present method has a high convergence order even for multiple roots by using the Pad6 approximation. Keywords: Root finding algorithm, polynomial equation, simultaneous Iterative method, Pad6 approximation.
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A high-order Iterative Formula for simultaneous determination of zeros of a polynomial
Journal of Computational and Applied Mathematics, 1991Co-Authors: Tetsuya Sakurai, Tatsuo Torii, Hiroshi SugiuraAbstract:Abstract We propose a hybrid method to determine all the zeros of a polynomial simultaneously, by combining the single-root method and the simultaneous one. The present method has a high convergence order even for multiple roots by using the Pade approximation.
