The Hessian matrix of Lagrange function

Chen, Pingge; Peng, Yuejian; Wang, Suijie

doi:10.1016/j.laa.2017.06.012

Cited by 8 publications

(3 citation statements)

References 5 publications

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“…In order to go from configurational space to phase space, a Legendre transformation is required, such that when J ((q i , q j ) −→ (q i , p i )) the det(J ) = 0 ( where J is the Jacobian). The Hessian condition demands that the following matrix, given by W i j = ∂ 2 L ∂ qi ∂ q j is non-singular [21]. This means that, det(W i j ) = 0.…”

Section: The Hessian Conditionmentioning

confidence: 99%

Free Fractional Gauge Fields: An Elementary Model Based on the Standard Model (SM)

Eastmond

2024

Preprint

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We study the Lagrangian density for freely propagating gauge fields on the basis of the Stan- dard Model (SM); namely its fractional counterpart. From this, we attain some free fractional Klein- Gordon equations, associated with the electromagnetic, weak, and strong forces. In addition to that, we verify that the Lagrange density is gauge invariant by virtue of the fractional Hessian condition. Also, using the fractional energy density we establish the fractional continuity equation for the freely propa- gating gauge bosons. And finally, a fractional analog of the Riemann-Silberstein vector and its equation is presented. Hence, we formulate fractional analogs of the Riemann-Silberstein and gravitoelectro- magnetic equations, which are compared to the fractional Maxwell’s equations.

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Section: The Hessian Conditionmentioning

confidence: 99%

Free Fractional Gauge Fields: An Elementary Model Based on the Standard Model (SM)

Eastmond

2024

Preprint

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“…The model is a piecewise continuous differentiable probability distribution, which can be matched with other point cloud data by the Hessian matrix method [29] without solving the complex correspondence problem directly. The result of the registration is shown in Figure 5; it is completed when the convergence conditions are reached.…”

Section: Lidar Odometrymentioning

confidence: 99%

Three-Dimensional Lidar Localization and Mapping with Loop-Closure Detection Based on Dense Depth Information

Yang

Deng

et al. 2023

Mathematics

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This paper presents a novel lidar SLAM system for localizing a mobile robot to build a map of the environment. To identify the unknown transform matrix, we design a new scan-matching approach, in which a point cloud segmentation algorithm is additionally integrated. Different from the traditional normal distribution transform algorithm for point cloud registration, our newly proposed one additionally incorporates a ground point remover and a point cloud segmentation method. By employing the point cloud segmentation algorithm to divide the point cloud space into different cells, the newly proposed algorithm can guarantee the continuity and convergence of the cost function. To tackle the recognition difficulties that the camera-based loop-closure detection heavily depends on the environment’s appearance, a depth-completion algorithm is introduced to fuse sensor data to ensure the robustness of the algorithm. Moreover, the bags of binary words (DBoW) are adopted to improve the image-matching quality. Finally, experimental results are presented to illustrate the effectiveness of the proposed system.

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“…Since the Hessian matrix of the contrast function [35] is a diagonal matrix under the whiteness constraint, the following simple learning rule can be obtained by applying Newton's method:…”

Section: Fast Iva Algorithmmentioning

confidence: 99%

An Efficient Convolutional Blind Source Separation Algorithm for Speech Signals under Chaotic Masking

et al. 2021

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As the main method of information transmission, it is particularly important to ensure the security of speech communication. Considering the more complex multipath channel transmission situation in the wireless communication of speech signals and separating or extracting the source signal from the convolutional signal are crucial steps in obtaining source information. In this paper, chaotic masking technology is used to guarantee the transmission safety of speech signals, and a fast fixed-point independent vector analysis algorithm is used to solve the problem of convolutional blind source separation. First, the chaotic masking is performed before the speech signal is sent, and the convolutional mixing process of multiple signals is simulated by impulse response filter. Then, the observed signal is transformed to the frequency domain by short-time Fourier transform, and instantaneous blind source separation is performed using a fast fixed-point independent vector analysis algorithm. The algorithm can preserve the high-order statistical correlation between frequencies to solve the permutation ambiguity problem in independent component analysis. Simulation experiments show that this algorithm can efficiently complete the blind extraction of convolutional signals, and the quality of recovered speech signals is better. It provides a solution for the secure transmission and effective separation of speech signals in multipath transmission channels.

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The Hessian matrix of Lagrange function

Cited by 8 publications

References 5 publications

Free Fractional Gauge Fields: An Elementary Model Based on the Standard Model (SM)

Free Fractional Gauge Fields: An Elementary Model Based on the Standard Model (SM)

Three-Dimensional Lidar Localization and Mapping with Loop-Closure Detection Based on Dense Depth Information

An Efficient Convolutional Blind Source Separation Algorithm for Speech Signals under Chaotic Masking

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