scholarly journals A Least Squares Computational Method for the Scattering Amplitude

1988 ◽  
Vol 41 (1) ◽  
pp. 47 ◽  
Author(s):  
JN Das
Keyword(s):  
Least Squares ◽  
Numerical Computation ◽  
Scattering Amplitude ◽  
High Accuracy ◽  
Computational Method ◽  
Partial Support ◽  
Numerical Instabilities

A new least squares computational method for the scattering amplitude is proposed. This may be applied without difficulty to atomic and other scattering computations. The approach is expected to give converged results of high accuracy and also to be free from major numerical instabilities. As an example a numerical computation is carried out following the method and some results are presented in partial support of the claim.

scholarly journals An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology

2021 ◽  
Author(s):  
Karl Kunisch ◽  
Philip Trautmann
Keyword(s):  
Inverse Problem ◽  
Least Squares ◽  
Eikonal Equation ◽  
State Equation ◽  
High Accuracy ◽  
Well Posedness ◽  
Numerical Examples ◽  
Marquardt Method ◽  
Math Biol ◽  
Levenberg Marquardt

AbstractIn this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg–Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033–2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.

Effects of Pressure Ports Layout on Angle of Attack and Sideslip Estimation in the Flush Air Data System

2011 ◽  
Vol 383-390 ◽  
pp. 2996-3000
Author(s):  
Fu Li ◽  
Zhen Luo
Keyword(s):  
Least Squares ◽  
Angle Of Attack ◽  
Inertial Navigation ◽  
Nonlinear Least Squares ◽  
High Accuracy ◽  
Data System ◽  
Evaluation Function ◽  
Theory Evaluation ◽  
Sideslip Estimation ◽  
Radiation Type

Flush air data system (FADS) have been successfully used on the nose tip of large manned/unmanned air vehicles instead of a traditional noseboom air data system. In order to integrate FADS with strapdown inertial navigation, high accuracy of angle of attack and sideslip is required. The estimated accuracy of angle of attack and sideslip in three types of FADS, which have different pressure ports layout, is compared using the nonlinear least squares theory. Evaluation function is provided to evaluate the accuracy of angle of attack and sideslip in different pressure ports layout. The results show that more sensors and radiation-type can provide high accuracy.

The phase-functions method and scalar amplitude of nucleon–nucleon scattering

2016 ◽  
Vol 25 (11) ◽  
pp. 1650088
Author(s):  
V. I. Zhaba
Keyword(s):  
Single Channel ◽  
Scattering Amplitude ◽  
Nucleon Nucleon ◽  
Phase Shifts ◽  
Computational Method ◽  
Nucleon Scattering ◽  
The Difference ◽  
Scalar Scattering ◽  
Scalar Amplitude ◽  
Phase Functions

A known phase-functions method (PFM) has been considered for calculation of a single-channel nucleon–nucleon scattering. The following partial waves of a nucleon–nucleon scattering have been considered using the phase shifts by PFM: 1S0-, 3P0-, 3P1-, 1D2-, 3F3-states for nn-scattering, 1S0-, 3P0-, 3P1-, 1D2-states for pp-scattering and 1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-states for np-scattering. The calculations have been carried out using phenomenological nucleon–nucleon Nijmegen group potentials (NijmI, NijmII, Nijm93 and Reid93) and Argonne v18 potential. The scalar scattering amplitude has been calculated using the obtained phase shifts. Our results are not much different from those obtained by using the known phase shifts published in other papers. The difference between calculations depending on a computational method of phase shifts makes: for real (imaginary) parts 0.14–4.36% (0.16–4.05%) for NijmI. 0.02–4.79% (0.08–3.88%) for NijmII. 0.01–5.49% (0.01–4.14%) for Reid93 and 0.01–5.11% (0.01–2.40%) for Argonne v18 potentials.

scholarly journals High-Sensitivity Determination of Nutrient Elements in Panax notoginseng by Laser-induced Breakdown Spectroscopy and Chemometric Methods

Molecules ◽  
2019 ◽  
Vol 24 (8) ◽  
pp. 1525 ◽  
Author(s):  
Tingting Shen ◽  
Weijiao Li ◽  
Xi Zhang ◽  
Wenwen Kong ◽  
Fei Liu ◽  
...  
Keyword(s):  
Chinese Medicine ◽  
Traditional Chinese Medicine ◽  
Least Squares ◽  
Panax Notoginseng ◽  
High Accuracy ◽  
Laser Induced Breakdown Spectroscopy ◽  
Quantitative Detection ◽  
Breakdown Spectroscopy ◽  
Laser Induced Breakdown

High-accuracy and fast detection of nutritive elements in traditional Chinese medicine Panax notoginseng (PN) is beneficial for providing useful assessment of the healthy alimentation and pharmaceutical value of PN herbs. Laser-induced breakdown spectroscopy (LIBS) was applied for high-accuracy and fast quantitative detection of six nutritive elements in PN samples from eight producing areas. More than 20,000 LIBS spectral variables were obtained to show elemental differences in PN samples. Univariate and multivariate calibrations were used to analyze the quantitative relationship between spectral variables and elements. Multivariate calibration based on full spectra and selected variables by the least absolute shrinkage and selection operator (Lasso) weights was used to compare the prediction ability of the partial least-squares regression (PLS), least-squares support vector machines (LS-SVM), and Lasso models. More than 90 emission lines for elements in PN were found and located. Univariate analysis was negatively interfered by matrix effects. For potassium, calcium, magnesium, zinc, and boron, LS-SVM models based on the selected variables obtained the best prediction performance with Rp values of 0.9546, 0.9176, 0.9412, 0.9665, and 0.9569 and root mean squared error of prediction (RMSEP) of 0.7704 mg/g, 0.0712 mg/g, 0.1000 mg/g, 0.0012 mg/g, and 0.0008 mg/g, respectively. For iron, the Lasso model based on full spectra obtained the best result with an Rp value of 0.9348 and RMSEP of 0.0726 mg/g. The results indicated that the LIBS technique coupled with proper multivariate chemometrics could be an accurate and fast method in the determination of PN nutritive elements for traditional Chinese medicine management and pharmaceutical analysis.

Modified wavelet method for solving fractional variational problems

2020 ◽  
pp. 107754632093202
Author(s):  
Haniye Dehestani ◽  
Yadollah Ordokhani ◽  
Mohsen Razzaghi
Keyword(s):  
Error Analysis ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Variational Problems ◽  
High Accuracy ◽  
Construction Method ◽  
Computational Method ◽  
Wavelet Method ◽  
Fractional Variational Problems ◽  
Operational Matrix Of Integration

In this article, a newly modified Bessel wavelet method for solving fractional variational problems is considered. The modified operational matrix of integration based on Bessel wavelet functions is proposed for solving the problems. In the process of computing this matrix, we have tried to provide a high-accuracy operational matrix. We also introduce the pseudo-operational matrix of derivative and the dual operational matrix with the coefficient. Also, we investigate the error analysis of the computational method. In the examples section, the behavior of the approximate solutions with respect to various parameters involved in the construction method is tested to illustrate the efficiency and accuracy of the proposed method.

scholarly journals On the Geometric Mean Method for Incomplete Pairwise Comparisons

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1873
Author(s):  
Konrad Kułakowski
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Geometric Mean ◽  
Computational Method ◽  
Pairwise Comparisons ◽  
Similar Relationship ◽  
Final Solution ◽  
The Difference ◽  
The Relationship ◽  
Theoretical Considerations

One of the most popular methods of calculating priorities based on the pairwise comparisons matrices (PCM) is the geometric mean method (GMM). It is equivalent to the logarithmic least squares method (LLSM), so some use both names interchangeably, treating it as the same approach. The main difference, however, is in the way the calculations are done. It turns out, however, that a similar relationship holds for incomplete matrices. Based on Harker’s method for the incomplete PCM, and using the same substitution for the missing entries, it is possible to construct the geometric mean solution for the incomplete PCM, which is fully compatible with the existing LLSM for the incomplete PCM. Again, both approaches lead to the same results, but the difference is how the final solution is computed. The aim of this work is to present in a concise form, the computational method behind the geometric mean method (GMM) for an incomplete PCM. The computational method is presented to emphasize the relationship between the original GMM and the proposed solution. Hence, everyone who knows the GMM for a complete PCM should easily understand its proposed extension. Theoretical considerations are accompanied by a numerical example, allowing the reader to follow the calculations step by step.

scholarly journals Lithium-Ion Battery Parameters and State of Charge Joint Estimation Using Bias Compensation Least Squares and the Alternate Algorithm

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Wei Xiong ◽  
Yimin Mo ◽  
Cong Yan
Keyword(s):  
Least Squares ◽  
Computational Efficiency ◽  
High Accuracy ◽  
State Of Charge ◽  
Joint Estimation ◽  
Model Parameters ◽  
Battery Management System ◽  
Battery Management ◽  
Soc Estimation ◽  
Bias Compensation

For safe and efficient operation of electric vehicles (EVs), battery management system is essential. Nevertheless, a challenge lying in battery management systems is how to obtain an algorithm for state of charge (SOC) estimation that has both high accuracy and low computational cost. For this purpose, the battery parameters and SOC joint estimation algorithm based on bias compensation least squares and alternate (BCLS-ALT) algorithm are proposed in this paper. The battery model parameters are identified online using the bias compensation least squares (BCLS), while the SOC is estimated applying the alternate (ALT) algorithm, which can switch the computational logic between H-infinity filter (HIF) and ampere-hour integral (AHI) to improve the computational efficiency and accuracy. The experimental results show that the accuracy of the SOC estimated by the BCLS-ALT algorithm is the highest, and the computational efficiency is also high, with the switching threshold SOCALT being set to 25%. Despite the 20% initial error and the 10% current drift, the proposed BCLS-ALT algorithm can obtain high accuracy and robustness of SOC estimation under different ambient temperatures and dynamic load profiles.

Damage Identification of Structure Based on RBF Neural Network

2013 ◽  
Vol 753-755 ◽  
pp. 2356-2359
Author(s):  
Cheng Gang Zhen ◽  
Xiang Ting Chong
Keyword(s):  
Neural Network ◽  
Least Squares ◽  
Health Monitoring ◽  
Damage Identification ◽  
Rbf Neural Network ◽  
High Accuracy ◽  
Learning Method ◽  
Test Results ◽  
Health Monitoring System ◽  
Orthogonal Least Squares

Health monitoring of the structure is a topic widely concerned and researched in the fields of technology and engineering at home and abroad. Damage identification of structure is an important aspect of the whole health monitoring system. In this paper, the RBF neural network with the effect of bionic is used to the extent, location and area recognition of the damage on the structure with single damage. The method of orthogonal least squares (OLS) is used as the learning method of the network. The test results show that the RBF neural network and the learning method of OLS can identify the damage status of the structure quickly and effectively with high accuracy.

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