## Numerical Comparison(数值比较)研究综述

Numerical Comparison 数值比较 - Numerical comparisons with other techniques show that this methodology can be useful in practical statistical modeling and analysis helping to researchers and managers in making meaningful decisions.^{[1]}Numerical comparisons are made among the classical, i.

^{[2]}Robustness of this estimation scheme is also demonstrated through a numerical comparison against some state-of-the-art nonlinear attitude estimation schemes.

^{[3]}Numerical comparisons demonstrate that the exponential integrators can obtain high accuracy and efficiency for solving large-scale systems of stiff Riccati differential equations.

^{[4]}A numerical comparison of the blood flow in a bioprosthesis connected to the main vascular bed using the «end-to-end» and «end-to-side» methods (bypass) taking into account the heart rate and blood pressure was performed.

^{[5]}The study found that through the numerical comparison of the experiment combined with the simulation analysis of Cog Tool and the target interaction experiment, the intrinsic cognitive law of the user in the interaction process was extracted.

^{[6]}The relations between the left and right states of the shock wave, rarefaction wave, and contact discontinuity are also discussed, so that the exact solution of the 1D Riemann problem could be derived and used for the numerical comparisons.

^{[7]}The numerical comparison is first carried out using real-world face-to-face dynamical networks collected in a high school, following by sequential multi-layer networks, generated relying on the Barabasi-Albert model emulating the department of Computing at Imperial College London in the UK as an example.

^{[8]}Numerical comparisons allow us to conclude that the proposed CA-system, which is based on simple arithmetic operations, achieves the same results that a reference model based on the well known d'Alembert one-dimensional discrete wave solution, with a Mean Square Error (MSE) in the order of 10−13.

^{[9]}Finally, to assess vibration isolation effectiveness and local stability behavior of trapezoidal CPVAs, a numerical comparison with the tautochrone parallel pendulum and results of multibody dynamics simulation are discussed.

^{[10]}Numerical comparisons are also provided.

^{[11]}Furthermore, differences between original and reconstructed animation are minimal, as evidenced by visual and numerical comparisons.

^{[12]}Numerical comparisons have made to show the performance of the proposed methods, as shown in the illustrative examples.

^{[13]}The effectiveness of the proposed L3Fnet is supported by both visual and numerical comparisons on this dataset.

^{[14]}Numerical comparisons with the two best-known methods demonstrate the efficiency of our method.

^{[15]}Finally, a numerical comparison and a practical examples are provided to demonstrate the validity of the developed finite-time control algorithm.

^{[16]}Through analytical and numerical comparisons, much more bifurcations and dynamical behaviors can be obtained and preserved by using the NSFD scheme, in which the integral step size can be chosen larger relatively due to its better stability and convergence than those in the forward Euler scheme.

^{[17]}Arguably the first outflow of probabilistic thinking in medicine was to evaluate the effects of smallpox inoculation in 18th-century England: numerical comparisons of death rates of inoculated and uninoculated groups were made by mathematically inclined clinicians such as James Jurin, Secretary of the Royal Society.

^{[18]}Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.

^{[19]}The effectiveness of our method is evaluated with numerical comparisons to existing techniques and through examples of ensemble and multivariate datasets.

^{[20]}An Eemian age is supported by the numerical comparison with the Beerenmosli (MIS 5e) and Meikirch 3 (MIS 7a) reference records.

^{[21]}Finally, a numerical comparison is given to verify validity and effectiveness of the proposed approach.

^{[22]}A numerical comparison is carried out with a total of 546 data sets.

^{[23]}: A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modeling, Journal of Geophysical Research: Earth Surface, 109, https://doi.

^{[24]}Numerical comparisons show that the logarithmic-barrier path-following method significantly outperforms the convex-quadratic-penalty path-following method.

^{[25]}We also perform an analytical and numerical comparison of LP NNLL + NLP LL resummation in softcollinear effective theory and direct QCD, where we achieve excellent analytical and numerical agreement once the NLP LL terms are included in both formalisms.

^{[26]}Numerical comparison between the models is generally good.

^{[27]}Thus, this paper presents an analysis on numerical comparison between common method and the other methods.

^{[28]}Under other situations, numerical comparisons with CPLEX 12.

^{[29]}A numerical comparison with the published works is conducted to verify the accuracy of the present study.

^{[30]}We frame linear factor models for asset pricing in a machine learning context and consider a numerical comparison of their performance against ordinary least squares linear regression over a dataset of anomaly portfolios.

^{[31]}Finally, numerical comparisons are presented to validate the routines.

^{[32]}Numerical comparisons are provided to demonstrate the effectiveness of the proposed strategies.

^{[33]}On test examples simulating the spatial inhomogeneity of the radiation field, a numerical comparison of the proposed method with some diffusion-type methods on the initial gas-dynamic and adapted computational meshes is carried out.

^{[34]}Numerical comparisons are performed to verify the convergence of the modified RPIM and the accuracy of iteration method in postbuckling path analysis.

^{[35]}Visual and numerical comparison of the concrete strength values obtained from isotherms gave an understanding of the degree of influence of sample heating on strength development.

^{[36]}Finally, a comprehensive analytical and numerical comparison of three illustrative examples is conducted to show that the proposed results are less conservative than the existing work.

^{[37]}We provide some numerical comparisons to illustrate our results.

^{[38]}Finally, numerical comparisons with the results in literature validate the effectiveness and accuracy of the proposed method.

^{[39]}The numerical comparison is first carried out using real-world face-to-face dynamic networks collected in a high school, followed by sequential multi-layer networks generated relying on the Barabasi-Albert model emulating large-scale social networks with several communities.

^{[40]}

与其他技术的数值比较表明，这种方法可用于实际的统计建模和分析，帮助研究人员和管理人员做出有意义的决策。

^{[1]}在经典之间进行数值比较，i。

^{[2]}通过与一些最先进的非线性姿态估计方案的数值比较，也证明了该估计方案的稳健性。

^{[3]}数值比较表明，指数积分器在求解大尺度刚性Riccati微分方程组时可以获得较高的精度和效率。

^{[4]}在考虑心率和血压的情况下，使用“端对端”和“端对端”方法（旁路）对连接到主血管床的生物假体中的血流进行了数值比较。

^{[5]}研究发现，通过实验的数值比较，结合Cog Tool的仿真分析和目标交互实验，提取了用户在交互过程中的内在认知规律。

^{[6]}还讨论了冲击波、稀疏波和接触不连续的左右状态之间的关系，从而可以推导出一维黎曼问题的精确解并用于数值比较。

^{[7]}数值比较首先使用在一所高中收集的现实世界的面对面动态网络进行，然后是基于模拟伦敦帝国理工学院计算系的 Barabasi-Albert 模型生成的顺序多层网络以英国为例。

^{[8]}数值比较使我们得出结论，所提出的基于简单算术运算的 CA 系统与基于众所周知的 d'Alembert 一维离散波解的参考模型具有相同的结果，均方误差 ( MSE）在 10−13 的数量级。

^{[9]}最后，为了评估梯形 CPVA 的隔振效果和局部稳定性行为，讨论了与等时线平行摆的数值比较和多体动力学模拟的结果。

^{[10]}还提供了数值比较。

^{[11]}此外，原始动画和重建动画之间的差异很小，视觉和数字比较证明了这一点。

^{[12]}如示例性示例所示，已进行数值比较以显示所提出方法的性能。

^{[13]}所提出的 L3Fnet 的有效性得到了对该数据集的视觉和数值比较的支持。

^{[14]}与两种最著名的方法的数值比较证明了我们方法的效率。

^{[15]}最后，通过数值比较和实例来证明所开发的有限时间控制算法的有效性。

^{[16]}通过解析和数值比较，使用NSFD格式可以获得和保留更多的分岔和动力学行为，其中积分步长可以选择相对较大，因为它比前向欧拉格式具有更好的稳定性和收敛性。

^{[17]}可以说，医学概率思维的第一次外流是评估 18 世纪英格兰接种天花疫苗的效果：由具有数学倾向的临床医生（如皇家学会秘书詹姆斯·朱林）对接种和未接种人群的死亡率进行了数值比较。

^{[18]}通过数值比较和多准则决策问题，我们表明所提出的距离度量是合理有效的。

^{[19]}我们的方法的有效性通过与现有技术的数值比较以及集成和多变量数据集的示例进行评估。

^{[20]}与 Beerenmosli (MIS 5e) 和 Meikirch 3 (MIS 7a) 参考记录的数值比较支持了 Eemian 时代。

^{[21]}最后通过数值比较验证了所提方法的有效性和有效性。

^{[22]}对总共 546 个数据集进行了数值比较。

^{[23]}：冰盖和冰川建模中使用的斯托克斯方程近似值的数值比较，地球物理研究杂志：地球表面，109，https://doi。

^{[24]}数值比较表明，对数障碍路径跟踪方法明显优于凸二次惩罚路径跟踪方法。

^{[25]}我们还对软共线有效理论和直接 QCD 中的 LP NNLL + NLP LL 重新求和进行了分析和数值比较，一旦 NLP LL 项包含在两种形式中，我们就可以实现出色的分析和数值一致性。

^{[26]}模型之间的数值比较通常很好。

^{[27]}因此，本文对常用方法与其他方法的数值比较进行了分析。

^{[28]}在其他情况下，与 CPLEX 12 进行数值比较。

^{[29]}与已发表的作品进行了数值比较，以验证本研究的准确性。

^{[30]}我们在机器学习环境中为资产定价构建线性因子模型，并考虑将它们的性能与异常投资组合数据集上的普通最小二乘线性回归进行数值比较。

^{[31]}最后，给出了数值比较来验证例程。

^{[32]}提供了数值比较来证明所提出策略的有效性。

^{[33]}在模拟辐射场空间不均匀性的测试示例中，对所提出的方法与一些扩散型方法在初始气体动力学和自适应计算网格上进行了数值比较。

^{[34]}通过数值比较验证了修正RPIM的收敛性和后屈曲路径分析中迭代法的准确性。

^{[35]}从等温线获得的混凝土强度值的视觉和数值比较有助于了解样品加热对强度发展的影响程度。

^{[36]}最后，对三个说明性示例进行了全面的分析和数值比较，以表明所提出的结果不如现有工作保守。

^{[37]}我们提供了一些数值比较来说明我们的结果。

^{[38]}最后，与文献结果的数值比较验证了所提方法的有效性和准确性。

^{[39]}数值比较首先使用在高中收集的真实世界面对面动态网络进行，然后是基于 Barabasi-Albert 模型生成的连续多层网络，模拟具有多个社区的大规模社交网络。

^{[40]}

## Extensive Numerical Comparison 广泛的数值比较

By extensive numerical comparisons, we show that our algorithms outperform existing DAG learning methods in identifying causal graphical structures.^{[1]}Extensive numerical comparisons on several test networks illustrate that the proposed method outperforms other Riemannian optimization methods (Gradient Descent, Newton's), and achieves comparable performance with the traditional Newton-Raphson method, albeit besting it by a guarantee to convergence.

^{[2]}Through extensive numerical comparisons, we show that ARCS outperformed existing methods by a substantial margin, demonstrating its great advantage in structure learning of Bayesian networks from both observational and experimental data.

^{[3]}Extensive numerical comparisons of one- and two-dimensional (2D) cases are reported to verify the effectiveness of the proposed algorithm and the correctness of the theoretical analysis.

^{[4]}We validate the performance of all our schemes via extensive numerical comparisons.

^{[5]}Extensive numerical comparisons are made with 3D models built by structured mesh.

^{[6]}Through extensive numerical comparisons, we demonstrate that our method outperforms other competitors with big margins for finite samples, including oracle methods built upon the true sparsity of the underlying model.

^{[7]}Extensive numerical comparisons using real and synthetic data sets demonstrate that the proposed algorithm provides state-of-the-art performance in terms of computational accuracy and cpu time.

^{[8]}

通过广泛的数值比较，我们表明我们的算法在识别因果图形结构方面优于现有的 DAG 学习方法。

^{[1]}在几个测试网络上进行的大量数值比较表明，所提出的方法优于其他黎曼优化方法（梯度下降法、牛顿法），并实现了与传统牛顿-拉夫森方法相当的性能，尽管在保证收敛方面优于它。

^{[2]}nan

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^{[4]}nan

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^{[8]}

## Detailed Numerical Comparison 详细的数值比较

The detailed numerical comparison for spectral line shapes in the frame of both scalar and vector perturbation additions with and without jumping frequency field dependence for the linear and quadratic Stark effects is presented.^{[1]}Here we carry out a detailed numerical comparison of several FP approaches with the exact scattering kernel solution for a range of test problems assuming isotropic media and thermal electrons at various temperatures.

^{[2]}In the paper, detailed numerical comparisons are considered for the mixed-mode failure characteristics of different composite adhesively bonded joints with brittle/quasi-brittle adhesive using following failure models: cohesive zone model (CZM), virtual crack closure technology (VCCT), mixed-mode continuum damage model (MCDM) and finite fracture mechanics (FFM).

^{[3]}Detailed numerical comparison with existing methods based on projection to the constrained space indicates that the modified SAV schemes are more efficient, particularly for the multi-component BECs.

^{[4]}

给出了在标量和矢量微扰加法框架中谱线形状的详细数值比较，其中线性和二次斯塔克效应具有和不具有跳跃频率场依赖性。

^{[1]}在这里，我们针对假设各向同性介质和热电子在不同温度下的一系列测试问题，对几种 FP 方法与精确散射核解进行了详细的数值比较。

^{[2]}nan

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^{[4]}

## Comprehensive Numerical Comparison 综合数值比较

In this work, we provide a comprehensive numerical comparison of microring/disk modulators between the conventional, lateral pn junction and our vertical pn junction designs.^{[1]}A comprehensive numerical comparison and statistical analysis are carried out to investigate the performance of the proposed approaches.

^{[2]}42 045205) made by Ferreira D R, we carry out a comprehensive numerical comparison of the three known analytic expressions for the electrostatic potential of a uniformly charged triangle sheet.

^{[3]}We also conduct a comprehensive numerical comparison of the effects of different modulating factors, including the price and the proportion and variation of surviving quantity, in these two settings.

^{[4]}

在这项工作中，我们对传统的横向 pn 结和我们的垂直 pn 结设计之间的微环/盘调制器进行了全面的数值比较。

^{[1]}进行了全面的数值比较和统计分析，以研究所提出方法的性能。

^{[2]}nan

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^{[4]}

## Provide Numerical Comparison 提供数值比较

We also provide numerical comparisons in synthetic simulations and the real PROSAIL model, a popular RTM that combines land vegetation leaf and canopy modeling.^{[1]}Moreover, it provides numerical comparisons for unconstrained minimization using benchmark functions of the unified algorithm with certain heuristic intelligent optimization algorithms.

^{[2]}We provide numerical comparisons with a new benchmark formulation, the so-called converted dc (CDC) power flow model, using Monte Carlo simulations for two different IEEE case studies.

^{[3]}

我们还提供了合成模拟和真实 PROSAIL 模型中的数值比较，PROSAIL 是一种流行的 RTM，它结合了陆地植被叶和冠层建模。

^{[1]}此外，它使用统一算法的基准函数与某些启发式智能优化算法提供了无约束最小化的数值比较。

^{[2]}nan

^{[3]}

## Present Numerical Comparison 当前数值比较

The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures.^{[1]}In this talk we present the methodology, apply it to the estimation of canonical ensembles and present numerical comparisons of the standard particle filter estimates with those of the homotopy data assimilation.

^{[2]}Finally, we present numerical comparisons of our data-driven minimax regret model with data-driven models based on the Hurwicz criterion and with a minimax regret model based on partial statistical information on moments.

^{[3]}

这一贡献的目的是在有限元 (FE) 程序的一般框架中对几何非线性结构的模型阶约简方法进行数值比较。

^{[1]}</p><p>在本次演讲中，我们介绍了该方法，将其应用于规范集合的估计，并展示了标准粒子滤波器估计与同伦数据同化的数值比较。

^{[2]}nan

^{[3]}

## Computerized Numerical Comparison 计算机数值比较

We analyzed data from 397 adults who performed a computerized numerical comparison task, a computerized numerical order verification task (i.^{[1]}We analyzed data from 397 adults who performed a computerized numerical comparison task, a computerized numerical order verification task (i.

^{[2]}

我们分析了 397 名执行计算机化数字比较任务、计算机化数字顺序验证任务（i.

^{[1]}我们分析了 397 名执行计算机化数字比较任务、计算机化数字顺序验证任务（i.

^{[2]}

## Several Numerical Comparison 几个数值比较

To illustrate the performance of this family, several numerical comparisons are made with other third and higher order methods.^{[1]}Several numerical comparisons are carried out to verify a higher degree of accuracy based on the obtained scheme.

^{[2]}

为了说明这个系列的性能，我们与其他三阶和更高阶方法进行了一些数值比较。

^{[1]}基于所获得的方案，进行了几次数值比较以验证更高程度的准确性。

^{[2]}

## numerical comparison result 数值比较结果

Several confirmations were performed for analytical and numerical comparison results.^{[1]}Theoretical analysis and numerical comparison results further show that the AFT-ZNN model has better performance than the TT-ZNN model.

^{[2]}Furthermore, Jacobi neural network method has higher accuracy compared with the approximate analytical methods, the numerical comparison results further show the feasibility and effectiveness of the proposed method for solving the DAEs.

^{[3]}Visual and numerical comparison results demonstrate the effectiveness of our RALSR for data representation and classification.

^{[4]}

对分析和数值比较结果进行了几次确认。

^{[1]}理论分析和数值比较结果进一步表明，AFT-ZNN模型比TT-ZNN模型具有更好的性能。

^{[2]}nan

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^{[4]}

## numerical comparison task 数值比较任务

We analyzed data from 397 adults who performed a computerized numerical comparison task, a computerized numerical order verification task (i.^{[1]}We aimed to compare the influence of sex in functional brain connectivity and behavioral measures in a numerical comparison task.

^{[2]}We analyzed data from 397 adults who performed a computerized numerical comparison task, a computerized numerical order verification task (i.

^{[3]}Adapting a numerical comparison task to a negative priming paradigm, we aimed to provide new evidence that inhibitory control processes are involved in numerical comparison.

^{[4]}

我们分析了 397 名执行计算机化数字比较任务、计算机化数字顺序验证任务（i.

^{[1]}我们的目的是在数值比较任务中比较性别对功能性大脑连接和行为测量的影响。

^{[2]}我们分析了 397 名执行计算机化数字比较任务、计算机化数字顺序验证任务（i.

^{[3]}nan

^{[4]}

## numerical comparison show 数值比较展示

Numerical comparison shows that the new method is remarkably effective for solving systems of nonlinear equations.^{[1]}Numerical comparison shows the effectiveness of the proposed methods.

^{[2]}The numerical comparison shows its applicability and accuracy in simulating the turbulent atmospheric boundary layer (ABL) flows, which satisfy the requirements of the fluctuating wind characteristics, such as the wind speed spectrum and the spatial correlation, and successfully achieve the equilibrium status for the numerical simulation of the ABL flow.

^{[3]}The numerical comparison shows that the proposed chart prevails over the existing standard MCV chart for detecting small and moderate upward and downward MCV shifts.

^{[4]}

数值比较表明，新方法对于求解非线性方程组非常有效。

^{[1]}数值比较表明了所提出方法的有效性。

^{[2]}nan

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^{[4]}

## numerical comparison experiment 数值比较实验

In parts of numerical comparison experiments, it is shown that the PC-CVZNN model possesses faster convergence rate than fixed-parameter CVZNN models and other analogy neural networks with parameter-changing function, when applied to finding the solution of CV-LME-TVC.^{[1]}Numerical comparison experiments are illustrated to prove the validity of the conjunction of possibility measures under intuitionistic evidence sets.

^{[2]}

部分数值比较实验表明，PC-CVZNN模型在求解CV-LME-TVC时，比固定参数CVZNN模型和其他具有参数变化功能的类比神经网络具有更快的收敛速度。

^{[1]}举例说明了数值比较实验，以证明直觉证据集下可能性测度联合的有效性。

^{[2]}