scholarly journals On joint probabilistic constraints with Gaussian coefficient matrix

2011 ◽  
Vol 39 (2) ◽  
pp. 99-102 ◽  
Author(s):  
W. van Ackooij ◽  
R. Henrion ◽  
A. Möller ◽  
R. Zorgati
Keyword(s):  
Coefficient Matrix ◽  
Probabilistic Constraints ◽  
Gaussian Coefficient

Reconstruction of complex shaped crack from ECT signals based on a fast forward solver using an advanced multi-media element

2020 ◽  
Vol 64 (1-4) ◽  
pp. 621-629
Author(s):  
Yingsong Zhao ◽  
Cherdpong Jomdecha ◽  
Shejuan Xie ◽  
Zhenmao Chen ◽  
Pan Qi ◽  
...  
Keyword(s):  
Coefficient Matrix ◽  
Crack Edge ◽  
Numerical Accuracy ◽  
Gauss Point ◽  
Current Testing ◽  
Efficient Simulation ◽  
Shaped Crack ◽  
Multi Media ◽  
Profile Reconstruction ◽  
Crack Profile

In this paper, the conventional database type fast forward solver for efficient simulation of eddy current testing (ECT) signals is upgraded by using an advanced multi-media finite element (MME) at the crack edge for treating inversion of complex shaped crack. Because the analysis domain is limited at the crack region, the fast forward solver can significantly improve the numerical accuracy and efficiency once the coefficient matrices of the MME can be properly calculated. Instead of the Gauss point classification, a new scheme to calculate the coefficient matrix of the MME is proposed and implemented to upgrade the ECT fast forward solver. To verify its efficiency and the feasibility for reconstruction of complex shaped crack, several cracks were reconstructed through inverse analysis using the new MME scheme. The numerical results proved that the upgraded fast forward solver can give better accuracy for simulating ECT signals, and consequently gives better crack profile reconstruction.

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

scholarly journals Analysis of the Propagation in High-Speed Interconnects for MIMICs by Means of the Method of Analytical Preconditioning: A New Highly Efficient Evaluation of the Coefficient Matrix

2021 ◽  
Vol 11 (3) ◽  
pp. 933
Author(s):  
Mario Lucido
Keyword(s):  
Integral Equation ◽  
Integrated Circuits ◽  
High Speed ◽  
Coefficient Matrix ◽  
Single Step ◽  
Integral Theorem ◽  
Acceleration Technique ◽  
Cauchy Integral Theorem ◽  
Integral Equation Formulation ◽  
High Speed Interconnects

The method of analytical preconditioning combines the discretization and the analytical regularization of a singular integral equation in a single step. In a recent paper by the author, such a method has been applied to a spectral domain integral equation formulation devised to analyze the propagation in polygonal cross-section microstrip lines, which are widely used as high-speed interconnects in monolithic microwave and millimeter waves integrated circuits. By choosing analytically Fourier transformable expansion functions reconstructing the behavior of the fields on the wedges, fast convergence is achieved, and the convolution integrals are expressed in closed form. However, the coefficient matrix elements are one-dimensional improper integrals of oscillating and, in the worst cases, slowly decaying functions. In this paper, a novel technique for the efficient evaluation of such kind of integrals is proposed. By means of a procedure based on Cauchy integral theorem, the general coefficient matrix element is written as a linear combination of fast converging integrals. As shown in the numerical results section, the proposed technique always outperforms the analytical asymptotic acceleration technique, especially when highly accurate solutions are required.

scholarly journals Pansharpening of WorldView-2 Data via Graph Regularized Sparse Coding and Adaptive Coupled Dictionary

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3586
Author(s):  
Wenqing Wang ◽  
Han Liu ◽  
Guo Xie
Keyword(s):  
High Resolution ◽  
Sparse Representation ◽  
Sparse Coding ◽  
Spectral Response ◽  
Objective Evaluation ◽  
Coefficient Matrix ◽  
Image Patch ◽  
Subjective Analysis ◽  
High Resolution Image ◽  
Sparse Coefficient

The spectral mismatch between a multispectral (MS) image and its corresponding panchromatic (PAN) image affects the pansharpening quality, especially for WorldView-2 data. To handle this problem, a pansharpening method based on graph regularized sparse coding (GRSC) and adaptive coupled dictionary is proposed in this paper. Firstly, the pansharpening process is divided into three tasks according to the degree of correlation among the MS and PAN channels and the relative spectral response of WorldView-2 sensor. Then, for each task, the image patch set from the MS channels is clustered into several subsets, and the sparse representation of each subset is estimated through the GRSC algorithm. Besides, an adaptive coupled dictionary pair for each task is constructed to effectively represent the subsets. Finally, the high-resolution image subsets for each task are obtained by multiplying the estimated sparse coefficient matrix by the corresponding dictionary. A variety of experiments are conducted on the WorldView-2 data, and the experimental results demonstrate that the proposed method achieves better performance than the existing pansharpening algorithms in both subjective analysis and objective evaluation.

scholarly journals Adjoint-based exact Hessian computation

2021 ◽  
Author(s):  
Shin-ichi Ito ◽  
Takeru Matsuda ◽  
Yuto Miyatake
Keyword(s):  
Krylov Subspace ◽  
Hessian Matrix ◽  
Adjoint System ◽  
Coefficient Matrix ◽  
Scalar Function ◽  
Second Order ◽  
Subspace Method ◽  
Initial Value ◽  
Research Fields ◽  
Memory Efficiency

AbstractWe consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system having the Hessian as a coefficient matrix arises in many research fields such as optimization, Bayesian estimation, and uncertainty quantification. From the perspective of memory efficiency, these tasks often employ a Krylov subspace method that does not need to hold the Hessian matrix explicitly and only requires computing the multiplication of the Hessian and a given vector. One of the ways to obtain an approximation of such Hessian-vector multiplication is to integrate the so-called second-order adjoint system numerically. However, the error in the approximation could be significant even if the numerical integration to the second-order adjoint system is sufficiently accurate. This paper presents a novel algorithm that computes the intended Hessian-vector multiplication exactly and efficiently. For this aim, we give a new concise derivation of the second-order adjoint system and show that the intended multiplication can be computed exactly by applying a particular numerical method to the second-order adjoint system. In the discussion, symplectic partitioned Runge–Kutta methods play an essential role.

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

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