Determination of ZIP parameters with least squares optimization method

2009 ◽  
Author(s):  
M. Sadeghi ◽  
G. Abdollahi sarvi
Keyword(s):  
Least Squares ◽  
Optimization Method ◽  
Least Squares Optimization

scholarly journals Partial Least Squares Optimization Method and Path Analysis Integration for Chinese Medicine Data

2020 ◽  
Vol 32 (10) ◽  
pp. 3463
Author(s):  
Tianci Li ◽  
Wangping Xiong ◽  
Jianqiang Du ◽  
Bin Nie ◽  
Jigen Luo ◽  
...  
Keyword(s):  
Chinese Medicine ◽  
Path Analysis ◽  
Least Squares ◽  
Partial Least Squares ◽  
Optimization Method ◽  
Least Squares Optimization

scholarly journals PSEUDONORMAL OPTIMIZATION METHOD AND GEODESIC EQUATION CALCULATIONS

2020 ◽  
Vol 25 (3) ◽  
pp. 5-13
Author(s):  
Amridon G. Barliani ◽  
◽  
Galina A. Nefedova ◽  
Irina V. Karnetova ◽  
◽  
...  
Keyword(s):  
Least Squares ◽  
Optimization Method ◽  
Geodesic Equation ◽  
Computational Process ◽  
Pseudoinverse Matrix ◽  
Method Of Least Squares ◽  
Mathematical Algorithm ◽  
Least Squares Optimization ◽  
Correction Equations ◽  
Sequential Formation

The purpose of this paper is a comparative analysis of the methods of least squares and pseudonormal optimization on the example of equalization and estimation of the accuracy of the first-class triangulation link. Pseudonormal optimization is radically different from the traditional method of least squares optimization, since it leads to complex and cumbersome procedures for equalizing and evaluating the accuracy of the results of processing geodesic constructions due to complex formulas. A recurrent method of sequential formation of a pseudoinverse matrix of parametric correction equations is presented, which allows avoiding the time-consuming computational process of composing and solving normal equations. A mathematical algorithm for estimating the accuracy of the equalized parameters is considered. The analysis of the equation works has shown that the pseudonormal optimization method allows calculating the values of the equalized coordinates 4 times more accurately than the least squares optimization.

Determination of Pyridostigmine Bromide in Presence of its Related Impurities by Four Modified Classical Least Square Based Models: A Comparative Study

2020 ◽  
Vol 17 (1) ◽  
pp. 87-94
Author(s):  
Ibrahim A. Naguib ◽  
Fatma F. Abdallah ◽  
Aml A. Emam ◽  
Eglal A. Abdelaleem
Keyword(s):  
Comparative Study ◽  
Least Squares ◽  
Orthogonal Projection ◽  
Predictive Ability ◽  
Least Square ◽  
Projection To Latent Structures ◽  
Preprocessing Method ◽  
Spectral Residual ◽  
Latent Structures

: Quantitative determination of pyridostigmine bromide in the presence of its two related substances; impurity A and impurity B was considered as a case study to construct the comparison. Introduction: Novel manipulations of the well-known classical least squares multivariate calibration model were explained in detail as a comparative analytical study in this research work. In addition to the application of plain classical least squares model, two preprocessing steps were tried, where prior to modeling with classical least squares, first derivatization and orthogonal projection to latent structures were applied to produce two novel manipulations of the classical least square-based model. Moreover, spectral residual augmented classical least squares model is included in the present comparative study. Methods: 3 factor 4 level design was implemented constructing a training set of 16 mixtures with different concentrations of the studied components. To investigate the predictive ability of the studied models; a test set consisting of 9 mixtures was constructed. Results: The key performance indicator of this comparative study was the root mean square error of prediction for the independent test set mixtures, where it was found 1.367 when classical least squares applied with no preprocessing method, 1.352 when first derivative data was implemented, 0.2100 when orthogonal projection to latent structures preprocessing method was applied and 0.2747 when spectral residual augmented classical least squares was performed. Conclusion: Coupling of classical least squares model with orthogonal projection to latent structures preprocessing method produced significant improvement of the predictive ability of it.

scholarly journals Application of Derivative, Derivative Ratio, and Multivariate Spectral Analysis and Thin-Layer Chomatography-Densitometry for Determination of a Ternary Mixture Containing Drotaverine Hydrochloride, Caffeine, and Paracetamol

2007 ◽  
Vol 90 (2) ◽  
pp. 391-404 ◽  
Author(s):  
Fadia H Metwally ◽  
Yasser S El-Saharty ◽  
Mohamed Refaat ◽  
Sonia Z El-Khateeb
Keyword(s):  
Thin Layer ◽  
Least Squares ◽  
Ternary Mixture ◽  
Principal Component Regression ◽  
Pharmaceutical Preparations ◽  
Principal Component ◽  
Standard Addition ◽  
Drotaverine Hydrochloride ◽  
Assay Precision

Abstract New selective, precise, and accurate methods are described for the determination of a ternary mixture containing drotaverine hydrochloride (I), caffeine (II), and paracetamol (III). The first method uses the first (D1) and third (D3) derivative spectrophotometry at 331 and 315 nm for the determination of (I) and (III), respectively, without interference from (II). The second method depends on the simultaneous use of the first derivative of the ratio spectra (DD1) with measurement at 312.4 nm for determination of (I) using the spectrum of 40 μg/mL (III) as a divisor or measurement at 286.4 and 304 nm after using the spectrum of 4 μg/mL (I) as a divisor for the determination of (II) and (III), respectively. In the third method, the predictive abilities of the classical least-squares, principal component regression, and partial least-squares were examined for the simultaneous determination of the ternary mixture. The last method depends on thin-layer chromatography-densitometry after separation of the mixture on silica gel plates using ethyl acetatechloroformmethanol (16 + 3 + 1, v/v/v) as the mobile phase. The spots were scanned at 281, 272, and 248 nm for the determination of (I), (II), and (III), respectively. Regression analysis showed good correlation in the selected ranges with excellent percentage recoveries. The chemical variables affecting the analytical performance of the methodology were studied and optimized. The methods showed no significant interferences from excipients. Intraday and interday assay precision and accuracy values were within regulatory limits. The suggested procedures were checked using laboratory-prepared mixtures and were successfully applied for the analysis of their pharmaceutical preparations. The validity of the proposed methods was further assessed by applying a standard addition technique. The results obtained by applying the proposed methods were statistically analyzed and compared with those obtained by the manufacturer's method.

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