A shape-finding approach of tree-like structure based on grouping strategy and generalized inverse matrix theory

Structures ◽  
2021 ◽  
Vol 29 ◽  
pp. 1960-1966
Author(s):  
Guigang Tu ◽  
Chen Chen
Keyword(s):  
Generalized Inverse ◽  
Matrix Theory ◽  
Inverse Matrix ◽  
Grouping Strategy ◽  
Generalized Inverse Matrix

scholarly journals Generalized inverse matrix-exterior penalty function (GIM-EPF) algorithm for data processing of multi-wavelength pyrometer (MWP)

2018 ◽  
Vol 26 (20) ◽  
pp. 25706 ◽  
Author(s):  
Jiafeng Liang ◽  
Li Dai ◽  
Sheng Chen ◽  
Weihong Gu ◽  
Bo Peng ◽  
...  
Keyword(s):  
Data Processing ◽  
Penalty Function ◽  
Generalized Inverse ◽  
Inverse Matrix ◽  
Multi Wavelength ◽  
Generalized Inverse Matrix

FINDING THE BEST-FIT POLYNOMIAL APPROXIMATION IN EVALUATING DRILL DATA: THE APPLICATION OF A GENERALIZED INVERSE MATRIX / POSZUKIWANIE NAJLEPSZEJ ZGODNOŚCI W PRZYBLIŻENIU WIELOMIANOWYM WYKORZYSTANEJ DO OCENY DANYCH Z ODWIERTÓW – ZASTOSOWANIE UOGÓLNIONEJ MACIERZY ODWROTNEJ

2013 ◽  
Vol 58 (4) ◽  
pp. 1289-1300
Author(s):  
Dogan Karakus
Keyword(s):  
Polynomial Approximation ◽  
Generalized Inverse ◽  
Random Variables ◽  
High Order ◽  
Inverse Matrix ◽  
Polynomial Degree ◽  
Polynomial Approximations ◽  
Random Samples ◽  
Generalized Inverse Matrix ◽  
Computationally Intensive

Abstract In mining, various estimation models are used to accurately assess the size and the grade distribution of an ore body. The estimation of the positional properties of unknown regions using random samples with known positional properties was first performed using polynomial approximations. Although the emergence of computer technologies and statistical evaluation of random variables after the 1950s rendered the polynomial approximations less important, theoretically the best surface passing through the random variables can be expressed as a polynomial approximation. In geoscience studies, in which the number of random variables is high, reliable solutions can be obtained only with high-order polynomials. Finding the coefficients of these types of high-order polynomials can be computationally intensive. In this study, the solution coefficients of high-order polynomials were calculated using a generalized inverse matrix method. A computer algorithm was developed to calculate the polynomial degree giving the best regression between the values obtained for solutions of different polynomial degrees and random observational data with known values, and this solution was tested with data derived from a practical application. In this application, the calorie values for data from 83 drilling points in a coal site located in southwestern Turkey were used, and the results are discussed in the context of this study.

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