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Showing 1 to 20 of 55 for “"steepest descent"”.
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A study of the use of a steepest descent technique in the solution of the Hartree-Fock equations and its application to selected systems
McWeeny has developed a method which utilizes the steepest descent technique in solving the Hartree-Fock equations. The mathematical development is presented and discussed. The method achieves convergence for several otherwise recalcitrant systems. The following systems are investigated and …
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An Examination of the Strengths and Weaknesses of Newton's Method for Nonlinear Optimization
… algorithms. In particular we examine Newton and steepest descent methods, focusing primarily on Newton/quasi-Newton methods. Because Newton's method is primarily viewed as a root-finding method, we start with the basic root-finding algorithm for single variable functions and show its progression …
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Optical Precursor Behavior
… resulting from an application of the method of steepest descent to that field integral. For any parameter regime where steepest descents may be applied, this work gives iterative methods to determine saddle points which are both more accurate than the accepted results and to extend into regimes …
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ΙΣΗΜΕΡΙΝΕΣ ΚΙΝΗΣΕΙΣ ΦΟΡΤΙΣΜΕΝΩΝ ΣΩΜΑΤΙΔΙΩΝ ΣΕ ΑΠΟΜΟΝΩΜΕΝΑ ΜΑΓΝΗΤΙΚΑ ΖΕΥΓΗ ΥΛΙΚΩΝ ΣΩΜΑΤΩΝ
… PARTICLE IN A MAGNETIC-BINARY SYSTEM. USING THE STEEPEST DESCENT METHOD, THE PERMISSIBLE AREAS OFMOTION ARE DERIVED THROUGH THEIR ZERO-VELOCITY CONTOURS. THESE CONTOURS REVEAL A NUMBER OF EQUILIBRIUM POINTS ON EACH EQUATORIAL PLANE, THE STABILITY OF WHICH IS STUDIED BY MEANS OF THE CHARACTERISTIC …
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A study of optimal load flow using nonlinear programming
… methods was established. Among the methods, steepest descent was chosen as most attractive and a further study was performed. Results of this are presented and conclusions drawn to improve the economical operation of our power system utilities.
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Fast Multilevel Algorithms for the Electromagnetic Analysis of Quasi-Planar Structures
… solution techniques, based on a steepest-descent fast multipole (SDFMM) formulation, are developed for solving scattering problems involving large quasi-planar structures. These techniques promise to open the door to the full-wave analysis of complex quasi-planar structures to an …
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Computational fluid dynamic based optimisation of an industrial axial fan for rapid prototyping
… rotor blade geometry. The spherical quadratic steepest descent method is employed, which does not rely on any explicit line searches, as required by traditional steepest descent techniques. The rapid prototyping tool is finally applied to an under-performing base fan (Fan-D) which cannot meet a …
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Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach
… matrix representation, we follow the steepest descent method of matrix transformations developed by Deift and Zhou.
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Selection of Step Size for Total Variation Minimization in CT
… be used to recover the image. In this paper, the steepest descent method is employed to update the approximation of the image. We propose a way to estimate an optimal step size so that the total variation is minimized. A new minimization problem is also proposed. Numerical tests are included to …
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System simulation using digital stochastic computing structures.
… and the second circuit uses the method of steepest descent. Each circuit is analysed as a continuous system in the main text, but a discrete time analysis of each network is given in the appendices. Close attention is paid to the stability and convergence of each method. A well known linear …
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The direct determination of nonlinear displacements of arbitrarily supported shallow shells using mathematical programming techniques
… are evaluated. These include the method of steepest descent, the conjugate gradient method, the variable metric method and the generalized Newton-Raphson procedure. A combination of the conjugate gradient method and the generalized Newton-Raphson procedure is found most suitable. Results of …
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The application of a rainfall-runoff model to the Maury River Basin in Virginia
… the basin coefficients by the method of steepest descent. After minor modification the model was utilized to predict six hourly incremental runoff. By applying unit hydrograph theory, a streamflow hydrograph was computed. The model was tested for the August 1969 flood. Agreement between …
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Investigations into implementation of an iterative feedback tuning algorithm into microcontroller
… since it also employs ‘myopic’ gradient based steepest descent approach to parameter optimization. It is easier to implement in that its algorithm is not as complex as the IFT one, meaning that successful implementation of IFT algorithm in a microcontroller would obviously permit the …
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Methods of non-linear least squares estimation
… function (includes the well-known Method of Steepest Descent), 3) combination techniques - attempts to gain an improved rate of convergence through a combination of the above two procedures, 4) the methods of parallel tangents - a geometrical approach, 5) methods of conjugate directions - …
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Simulation of Adaptive Array Algorithms for CDMA Systems
… modulus algorithm (MT-LSCMA) and multitarget steepest-descent decision-directed (MT-SDDD) algorithm. It is shown from the simulation results that these two novel algorithms can outperform the other algorithms in all the test situations (e.g., AWGN channel, timing offset case, frequency offset …
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Stability analysis of gravity-driven viscosity-stratified coating flows
… proper ray-speed approach, originating from a steepest descent method to determine the perturbed film thickness, removed the interpretational quandary present in the classical spatial approach and corroborated the temporal linear stability results.
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Fast Sweeping Methods for Steady State Hyperbolic Conservation Problems and Numerical Applications for Shape Optimization and Computational Cell Biology
… waves at a specific wavelength, is solved by the steepest descent method. The method of steepest descent is a classical approach to find the minimum/maximum of an objective function or functional based on a first order approximation. The method works in spaces of any number of dimensions, even in …
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A Riemann-Hilbert Approach to the Kissing Polynomials
… an overview of the powerful non-commutative steepest descent technique developed by Deift and Zhou in the mid 1990s used to compute the asymptotics for oscillatory Riemann-Hilbert problems, which will be used extensively in Chapters 4 and 5. In Chapter 3, we utilize the Riemann-Hilbert …
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Stability Enhancement of the Microgrid under High-depth of Penetration of Electronically-coupled Resources
… formulation, a cluster eigen analysis, a steepest-descent optimization, and a discrete-event supervisor. An off-grid microgrid and a multi-microgrid system, are used for the reported studies. Feasibility of the SC real-time algorithms is demonstrated based on their implementation on an …
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Estratégias de inversão de multiparâmetros utilizando a equação completa da elastodinâmica
… methods to the 2D isotropic acoustic case: steepest-descent, two conjugated-gradients (PolakRibi`ere and Fletcher-Reeves) and the l-BFGS (Quasi-Newton). This analysis reinforces that the l-BFGS method, which makes Hessian approximations iteratively, is the one that better estimates the …
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