“…Linear Systems Computing An Fundamental Set of Solutions Second-Order Difference Equations Phase Space Diagrams Stability Notions Stability of Linear Systems The Trace-Determinant Plane Liapunov Functions for Nonlinear Maps Linear Systems Revisited Stability via Linearization Applications Appendix Bifurcation and Chaos in Two Dimensions Center Manifolds Bifurcation Hyperbolic Anosov Toral Automorphism Symbolic Dynamics The Horseshoe and Hénon Maps A Case Study: Extinction and Sustainability in Ancient Civilizations Appendix Fractals Examples of Fractals L-System The Dimension of a Fractal Iterated Function System Mathematical Foundation of Fractals The Collage Theorem and Image Compression The Julia and Mandelbrot Sets Introduction Mapping by Functions on the Complex Domain The Riemann Sphere The Julia Set Topological Properties of the Julia Set Newton's Method in the Complex Plane The Mandelbrot Set Bibliography Answers to Selected Problems Index.…”
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“…We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. …”
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“…In this paper we consider the iteratively regularized Gauss–Newton method (IRGNM) in its classical Tikhonov version as well as two further—Ivanov type and Morozov type—versions. …”
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“…OutbreakFinder can be downloaded for free at https://github.com/skypes/Newton-method-MDS.…”
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“…Good matching of the empirical and theoretical quantities was also confirmed using the quasi-Newton method. The article is a solution to the problem of the effective use of solar energy within transparent building partitions, while presenting a useful mathematical tool that determines potential thermal gains in various climatic conditions.…”
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“…To solve the cost function and filter out wrong feature matches, we build a robust pose solver using the Gauss–Newton method and Chi-Square test. To correct the drift of camera poses, we maintain a sliding-window framework to update the keyframe poses and related features. …”
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“…The artificial neural network trained using the quasi-Newton method demonstrates a capability for accurately estimating the redox potentials. …”
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“…In implementing Adaboost learning, the proposed algorithm employs an exponential criterion as a cost function and Newton's method for its optimization. In particular, we introduce an optimal selection of weak classifiers minimizing the cost function and derive the reinforced predictions based on a judicial confidence estimate to determine the classification results. …”
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“…This study also analyzes the conditions for uniqueness of the equilibrium solution. A Newton method is developed to solve the proposed model. …”
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“…Finally, the PBD method is more efficient and robust than the Newton method. Since it has sufficient visual plausibility and can realize real-time visualization, the simulation system developed by the PBD method effective for training crew members.…”
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“…Finally, a kd-tree is introduced into the ICP algorithm for point pair search, and the Gauss–Newton method is used to optimize the solution of nonlinear objective function of the algorithm to complete accurate registering of tunneling roadway point clouds. …”
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“…This study tests the dynamic quasi-Newton method for estimating the Jacobian matrix and optimizes the initialization coupling problem using the orthogonal moving method. …”
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“…In this work, we present an implementation that utilizes a matrix free in terms of the Jacobian matrix Gauss-Newton method and improves the scalability of the geostatistical inverse problem. …”
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“…We extracted the HSV color data from the point cloud color information and made the HSV distribution of the tangent plane continuous, and we used the genetic algorithm to optimize the point cloud color information consistently. The Gauss–Newton method was utilized to realize the optimal registration of color point clouds for the joint error function of color and geometry. …”
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“…Particle Swarm Optimization (PSO), a population based technique for stochastic search in a multidimensional space, has so far been employed successfully for solving a variety of optimization problems including many multifaceted problems, where other popular methods like steepest descent, gradient descent, conjugate gradient, Newton method, etc. do not give satisfactory results. …”
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“…In each step of the NMPC method the open-loop problem is solved with a projected quasi-Newton method. The controller is successfully tested in-silico on several patient parameter sets. …”
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“…The SLM method accounts for all lake sources and sinks, establishing a governing equation that can be solved using Newton's method. A benchmarking case study was conducted using a modified model setup in the LAK3 user manual. …”
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“…We present extensive numerical experiments to show the performance of the architecture and compare the proposed method with previous analytic algorithms, mainly the monotonicity-based shape reconstruction algorithm and iteratively regularized Gauss–Newton method.…”
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“…Recently, a multiple step-sizes fast gradient descent (MFGD) method has been proposed for optimizing NMF which accelerates MUR by searching the optimal step-size along the rescaled negative gradient direction with Newton's method. However, the computational cost of MFGD is high because 1) the high-dimensional Hessian matrix is dense and costs too much memory; and 2) the Hessian inverse operator and its multiplication with gradient cost too much time. …”
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