New Computational Methods for Solving Problems of the Astronomical Vessel Position

2005 ◽  
Vol 58 (2) ◽  
pp. 315-335 ◽  
Author(s):  
Tien-Pen Hsu ◽  
Chih-Li Chen ◽  
Jiang-Ren Chang
Keyword(s):  
Coordinate System ◽  
Computational Methods ◽  
Matrix Method ◽  
Iteration Scheme ◽  
Computation Method ◽  
Direct Computation ◽  
Celestial Navigation ◽  
Vector Algebra ◽  
The Matrix ◽  
Triangle Method

In this paper, a simplified and direct computation method formulated by the fixed coordinate system and relative meridian concept in conjunction with vector algebra is developed to deal with the classical problems of celestial navigation. It is found that the proposed approach, the Simultaneous Equal-altitude Equation Method (SEEM), can directly calculate the Astronomical Vessel Position (AVP) without an additional graphical procedure. The SEEM is not only simpler than the matrix method but is also more straightforward than the Spherical Triangle Method (STM). Due to tedious computation procedures existing in the commonly used methods for determining the AVP, a set of optimal computation procedures for the STM is also suggested. In addition, aimed at drawbacks of the intercept method, an improved approach with a new computation procedure is also presented to plot the celestial line of position without the intercept. The improved approach with iteration scheme is used to solve the AVP and validate the SEEM successfully. Methods of solving AVP problems are also discussed in detail. Finally, a benchmark example is included to demonstrate these proposed methods.

scholarly journals Determination of stoichiometric coefficients by the matrix method

2007 ◽  
Vol 61 (1) ◽  
pp. 18-22
Author(s):  
Goran Tadic ◽  
Branko Pejovic ◽  
Miladin Gligoric ◽  
Vladan Micic
Keyword(s):  
Matrix Equation ◽  
Matrix Method ◽  
Chemical Compounds ◽  
New Approach ◽  
Standard Methods ◽  
Vector Algebra ◽  
Chemical Equations ◽  
The Matrix ◽  
Chemical Equation

The problem of calculating stoichiometric coefficients in a chemical equation can be solved by standard methods and the method of multidimensional vector space, but good knowledge of vector algebra is required. In this paper, the authors proposed a matrix method and other treatment of the problem was given as the authors' own interpretation. A matrix was formed in the form of base using all the elements which take place in a chemical reaction, after which the matrixes of all the chemical compounds were determined based on numerical indexes and element symbols. This approach enables the setting of a principal matrix equation based on a mathematical approach. The solutions of this matrix equation are the desired stoichiometric coefficients that form a balanced equation. A new approach to tabular solving is presented. This method, compared to existing standard methods, is faster, simpler, and more effective, especially for complex chemical equations. The method was tasted on examples from inorganic chemistry and metallurgy.

scholarly journals Matrix Approach To The Direct Computation Method For The Solution of Fredholm Integro-Differential Equations of The Second Kind With Degenerate Kernels

CAUCHY ◽  
2020 ◽  
Vol 6 (3) ◽  
pp. 100-108
Author(s):  
Nathaniel Mahwash Kamoh ◽  
Geoffrey Kumlengand ◽  
Joshua Sunday
Keyword(s):  
Differential Equations ◽  
Computation Method ◽  
Matrix Approach ◽  
Algebraic Equations ◽  
Direct Computation ◽  
Closed Form Solutions ◽  
Linear Algebraic Equations ◽  
The Matrix ◽  
Sum Of Products ◽  
Finite Sum

In this paper, a matrix approach to the direct computation method for solving Fredholm integro-differential equations (FIDEs) of the second kind with degenerate kernels is presented. Our approach consists of reducing the problem to a set of linear algebraic equations by approximating the kernel with a finite sum of products and determining the unknown constants by the matrix approach. The proposed method is simple, efficient and accurate; it approximates the solutions exactly with the closed form solutions. Some problems are considered using maple programme to illustrate the simplicity, efficiency and accuracy of the proposed method.

scholarly journals Fast and Robust Orientation of Cryo-Electron Microscopy Images

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Guoliang Xu ◽  
Xia Wang ◽  
Ming Li ◽  
Zhucui Jing
Keyword(s):  
Sparse Matrix ◽  
Three Dimensional ◽  
Image Plane ◽  
Real Space ◽  
Computation Method ◽  
Common Line ◽  
The Matrix ◽  
Common Lines ◽  
The Common ◽  
Dimensional Object

AbstractWe present an efficient and reliable algorithm for determining the orientations of noisy images obtained fromprojections of a three-dimensional object. Based on the linear relationship among the common line vectors in one image plane, we construct a sparse matrix, and show that the coordinates of the common line vectors are the eigenvectors of the matrix with respect to the eigenvalue 1. The projection directions and in-plane rotation angles can be determined fromthese coordinates. A robust computation method of common lines in the real space using aweighted cross-correlation function is proposed to increase the robustness of the algorithm against the noise. A small number of good leading images, which have the maximal dissimilarity, are used to increase the reliability of orientations and improve the efficiency for determining the orientations of all the images. Numerical experiments show that the proposed algorithm is effective and efficient.

Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

2004 ◽  
Vol 59 (9) ◽  
pp. 621-622 ◽  
Author(s):  
Fatih Ucun ◽  
Vesile Gūçlü
Keyword(s):  
Gas Phase ◽  
Condensed Phase ◽  
Matrix Method ◽  
Solid Phase ◽  
Force Constants ◽  
Matrix Solution ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

scholarly journals Multivariate analytical methods for simultaneous estimation of Atenolol and Hydrochlorothiazide in bulk and tablet dosage form

2021 ◽  
Vol 6 (4) ◽  
pp. 205-208
Author(s):  
Sreenivasa Charan Archakam ◽  
Keerthisikha Palur ◽  
Praveen Kumar Arava
Keyword(s):  
Linear Regression ◽  
Matrix Method ◽  
Linear Regression Analysis ◽  
Molar Absorptivity ◽  
Simultaneous Estimation ◽  
Linear Regression Method ◽  
Spectrophotometric Methods ◽  
The Matrix ◽  
Ft Ir ◽  
Tablet Dosage

The present study aimed to develop simple, accurate and precise FTIR and UV spectrophotometric methods for the quantification of Atenolol and Hydrochlorothiazide in bulk and tablet dosage forms. FT-IR method like classical least squares (CLS) was developed within the range of 2366.69-3433.44; 1564.40-1673.30 cm- UV methods like Cramer’s matrix method (method-I) and linear regression analysis (Method II) were developed and they are based upon constructing the matrix set by using molar absorptivity values at 275.60 nm and 270.40 nm. The assay values for FTIR- CLS method were 102% and 108 % for Atenololand Hydrochlorothiazide respectively. Cramer’s matrix method results were found to be 95.15% and 104% for Atenolol and Hydrochlorothiazide respectively and for linear regression method they were found to be 98.50% and 106% (w/w).

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