Adaptive multidimensional interpolation using regularized linear splines

1993 ◽  
Author(s):  
Donald J. Bone
Keyword(s):  
Multidimensional Interpolation ◽  
Linear Splines

Modeling of photosynthesis light curves by linear splines

2019 ◽  
pp. 20-29
Author(s):  
Alexander S. Lelekov ◽  
Rudolf P. Trenkenshu
Keyword(s):  
Experimental Data ◽  
Chlorophyll A ◽  
Skeletonema Costatum ◽  
Light Flux ◽  
Photosynthesis Rate ◽  
Light Curves ◽  
External Irradiation ◽  
Exchange Reactions ◽  
Cell Adaptation ◽  
Linear Splines

The paper presents an example of the linear splines use to describe the photosynthesis light curves for microalgae culture. The main mathematical models of the relationship between photosynthesis rate and light are listed. Based on the previously formulated basic principles of modeling microalgae photobiosynthesis, a mathematical model is proposed that describes the dependence of the assimilation number of chlorophyll a on the value of the light flux by linear splines. The advantage of the proposed approach is a clear definition of the point of change of the limiting factor. It is shown that light-limited photosynthesis rate is determined not only by external irradiation, but also by the concentration of chlorophyll a. The light-saturated rate depends on the amount of a key enzyme complex, which limits the rate of energy exchange reactions in the cell. Verification of the proposed model on the example of the diatom microalgae Skeletonema costatum was carried out. It is shown that the higher the degree of cell adaptation to high irradiation, the better the photosynthesis curve is described by linear splines. If S. costatum cells are adapted to low irradiation, deviations of experimental data from the idealized broken line are observed, which are caused by changes in the pigment composition. When the experimental data are normalized, the cell adaptation factor is reduced, all points are described by a single broken line, which indicates the universality of the proposed approach.

GEOMETRIC THEORY OF MULTIDIMENSIONAL INTERPOLATION

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-16
Author(s):  
Evgeniy Konopatskiy
Keyword(s):  
Response Function ◽  
Algebraic Curves ◽  
Geometric Theory ◽  
Analytical Description ◽  
Geometric Interpretation ◽  
Affine Geometry ◽  
Mathematical Apparatus ◽  
Multidimensional Interpolation ◽  
Pass Through

The paper presents a geometric theory of multidimensional interpolation based on invariants of affine geometry. The analytical description of geometric interpolants is performed within the framework of the mathematical apparatus BN-calculation using algebraic curves that pass through preset points. A geometric interpretation of the interaction of parameters, factors, and the response function is presented, which makes it possible to generalize the geometric theory of multidimensional interpolation in the direction of increasing the dimension of space. The conceptual principles of forming the tree of the geometric interpolant model as a geometric basis for modeling multi-factor processes and phenomena are described.

Minimax Linear Splines

1992 ◽  
Author(s):  
Royce W. Soanes
Keyword(s):  
Linear Splines

Separation of Trend and Chaotic Components of Time Series and Estimation of Their Characteristics by Linear Splines

2018 ◽  
Vol 15 (2) ◽  
pp. 194-197 ◽  
Author(s):  
A. V. Kryanev ◽  
V. V. Ivanov ◽  
A. O. Romanova ◽  
L. A. Sevastyanov ◽  
D. K. Udumyan
Keyword(s):  
Time Series ◽  
Linear Splines

scholarly journals DQ-Frame Admittance Estimation of Three-Phase Converters with a Wide Range of Operating Points

2021 ◽  
Author(s):  
Hong Gong ◽  
xiongfei wang ◽  
Dongsheng Yang
Keyword(s):  
Error Estimation ◽  
Closed Loop ◽  
Estimation Method ◽  
Experimental Results ◽  
Multidimensional Interpolation ◽  
Three Phase ◽  
Wide Range ◽  
Linearized Model ◽  
Operating Points ◽  
Error Estimation Method

The <i>dq</i>-frame admittance of closed-loop controlled three-phase converters is a linearized model that is dependent on the operating points of the system. Yet, it is impractical to measure the converter admittance at all operating points. This paper, thus, proposes an approach to estimating the <i>dq</i>-frame admittance of three-phase converters at a wide range of operating points. The method applies multidimensional interpolation to a given set of admittance data, which is measured from the pre-defined operating points. The accuracy of interpolation is then evaluated by using the posterior error estimation method. The number of pre-defined operating points is next adjusted to find a good compromise between the accuracy and efficiency of the approach. Simulations and experimental results verify the effectiveness of the approach.<div><br></div>

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