scholarly journals Experimental Approach of the Asymptotic Computational Complexity of Shaders for Mobile Devices with OpenGL ES

2017 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Alex S. C. Lima ◽  
Edson A. C. Junior
Keyword(s):  
Computational Complexity ◽  
Least Squares ◽  
Mobile Devices ◽  
Experimental Approach ◽  
Critical Factor ◽  
Sampled Data ◽  
Method Of Least Squares ◽  
Opengl Es ◽  
Automatic Tool

The usage of mobile devices and increasingly realistic graphics is emerging, but the graphics performance is still a critical factor in games. There’s more hardware restriction on mobile devices than on a computer. Thus, this paper proposes an experimental approximation of the asymptotic computational complexity of miscellaneous vertex and fragment shaders for Android and iOS platforms. The asymptotic complexities of the shaders will be analyzed based on number of instructions per second and rendering time metrics, depending on the number of polygons rendered. By means of the adjusted curves is also possible to compare the performance of the devices used in this work, which are the Nexus 4, HTC One, iPhone 5s and iPad Air. Besides, an automatic tool – that plots the data and uses the method of least squares to adjust the values obtained – will be presented, being able to estimate which curve has better approximation to the sampled data.

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

2020 ◽  
pp. 60-73
Author(s):  
Yu V Nemirovskii ◽  
S V Tikhonov
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Nonlinear Differential Equations ◽  
Limit State ◽  
Algebraic Equations ◽  
Method Of Least Squares ◽  
Elasticity Limit ◽  
Limit Values ◽  
Symbolic Calculations ◽  
Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

scholarly journals Functional ratings in sports

2020 ◽  
Vol 16 (3) ◽  
pp. 183-191
Author(s):  
Brad Lowery ◽  
Abigail Slater ◽  
Kaison Thies
Keyword(s):  
Least Squares ◽  
Method Of Least Squares ◽  
Sports Teams ◽  
New Model ◽  
College Basketball ◽  
Division 1

AbstractIn this paper, we present a new model for ranking sports teams. Our model uses all scoring data from all games to produce a functional rating by the method of least squares. The functional rating can be interpreted as a team average point differential adjusted for strength of schedule. Using two team’s functional ratings we can predict the expected point differential at any time in the game. We looked at three variations of our model accounting for home-court advantage in different ways. We use the 2018–2019 NCAA Division 1 men’s college basketball season to test the models and determined that home-court advantage is statistically important but does not differ between teams.

scholarly journals Historical Note on the Method of Least Squares

Nature ◽  
1872 ◽  
Vol 6 (136) ◽  
pp. 101-102
Author(s):  
ASAPH HALL
Keyword(s):  
Least Squares ◽  
Historical Note ◽  
Method Of Least Squares

The Method of Least Squares

Nature ◽  
1872 ◽  
Vol 6 (138) ◽  
pp. 140-141
Author(s):  
J. W. L. GLAISHER
Keyword(s):  
Least Squares ◽  
Method Of Least Squares

Outlier removal method for the refinement of optical measured displacement field based on critical factor least squares and subdomain division

2021 ◽  
Author(s):  
Bo Wang ◽  
Chen Sun ◽  
Keming Zhang ◽  
Jubing Chen
Keyword(s):  
Least Squares ◽  
Displacement Field ◽  
Critical Factor ◽  
Least Square ◽  
Outlier Removal ◽  
Full Field ◽  
Removal Method ◽  
Strain Estimation ◽  
Data Points ◽  
Measured Displacement

Abstract As a representative type of outlier, the abnormal data in displacement measurement often inevitably occurred in full-field optical metrology and significantly affected the further evaluation, especially when calculating the strain field by differencing the displacement. In this study, an outlier removal method is proposed which can recognize and remove the abnormal data in optically measured displacement field. A iterative critical factor least squares algorithm (CFLS) is developed which distinguishes the distance between the data points and the least square plane to identify the outliers. A successive boundary point algorithm is proposed to divide the measurement domain to improve the applicability and effectiveness of the CFLS algorithm. The feasibility and precision of the proposed method are discussed in detail through simulations and experiments. Results show that the outliers are reliably recognized and the precision of the strain estimation is highly improved by using these methods.

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