Data Approximation by L1 Spline Fits with Free Knots

2021 ◽  
pp. 102064
Author(s):  
Ziteng Wang ◽  
Manfei Xie
Keyword(s):  
Data Approximation

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals Exact solutions of infinite dimensional total-variation regularized problems

2018 ◽  
Vol 8 (3) ◽  
pp. 407-443 ◽  
Author(s):  
Axel Flinth ◽  
Pierre Weiss
Keyword(s):  
Inverse Problems ◽  
Exact Solutions ◽  
Total Variation ◽  
Linear Mapping ◽  
Scattered Data Approximation ◽  
Convex Programs ◽  
Linear Measurements ◽  
Data Approximation ◽  
Infinite Dimensional ◽  
Finite Dimensional

Abstract We study the solutions of infinite dimensional inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary function. The first contribution describes the solution’s structure: we show that under mild assumptions, there always exists an $m$-sparse solution, where $m$ is the number of linear measurements of the signal. Our second contribution is about the computation of the solution. While most existing works first discretize the problem, we show that exact solutions of the infinite dimensional problem can be obtained by solving one or two consecutive finite dimensional convex programs depending on the measurement functions structures. We finish by showing an application on scattered data approximation. These results extend recent advances in the understanding of total-variation regularized inverse problems.

Measurement data approximation by pseudo-random sequences

2021 ◽  
Author(s):  
Alexey Levenets ◽  
Ruslan Bazhenov ◽  
Natalya Chalkina ◽  
Olga Chuyko ◽  
Zoya Arkhipova
Keyword(s):  
Measurement Data ◽  
Random Sequences ◽  
Data Approximation
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