Adaptive Interpolation Algorithm Based on a kd-Tree for the Problems of Chemical Kinetics with Interval Parameters

2019 ◽  
Vol 11 (4) ◽  
pp. 622-633 ◽  
Author(s):  
A. Yu. Morozov ◽  
D. L. Reviznikov ◽  
V. Yu. Gidaspov
Keyword(s):  
Chemical Kinetics ◽  
Interpolation Algorithm ◽  
Interval Parameters ◽  
Adaptive Interpolation

KD-Tree based adaptive interpolation algorithm for chemical kinetics problems with interval parameters

2018 ◽  
Vol 30 (12) ◽  
pp. 129-144
Author(s):  
A. Morozov ◽  
◽  
D. Reviznikov ◽  
V. Gidaspov ◽  
◽  
...  
Keyword(s):  
Chemical Kinetics ◽  
Interpolation Algorithm ◽  
Interval Parameters ◽  
Adaptive Interpolation

scholarly journals Sparse Grid Adaptive Interpolation in Problems of Modeling Dynamic Systems with Interval Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 298
Author(s):  
Alexander Yu Morozov ◽  
Andrey A. Zhuravlev ◽  
Dmitry L. Reviznikov
Keyword(s):  
Dynamic Systems ◽  
Materials Science ◽  
Sparse Grids ◽  
Interpolation Algorithm ◽  
Piecewise Polynomial Function ◽  
Interval Parameters ◽  
Adaptive Interpolation ◽  
Interval Uncertainties ◽  
Computational Materials ◽  
Interval Problems

The paper is concerned with the issues of modeling dynamic systems with interval parameters. In previous works, the authors proposed an adaptive interpolation algorithm for solving interval problems; the essence of the algorithm is the dynamic construction of a piecewise polynomial function that interpolates the solution of the problem with a given accuracy. The main problem of applying the algorithm is related to the curse of dimension, i.e., exponential complexity relative to the number of interval uncertainties in parameters. The main objective of this work is to apply the previously proposed adaptive interpolation algorithm to dynamic systems with a large number of interval parameters. In order to reduce the computational complexity of the algorithm, the authors propose using adaptive sparse grids. This article introduces a novelty approach of applying sparse grids to problems with interval uncertainties. The efficiency of the proposed approach has been demonstrated on representative interval problems of nonlinear dynamics and computational materials science.

scholarly journals Modeling of Dynamic Systems With Interval Parameters

2019 ◽  
Vol 09 (4) ◽  
pp. 5-31
Author(s):  
A.Y. Morozov ◽  
D.L. Reviznikov
Keyword(s):  
Dynamic Systems ◽  
Interval Analysis ◽  
Interpolation Algorithm ◽  
Interval Parameters ◽  
Estimates Of Solutions ◽  
Software Libraries ◽  
Adaptive Interpolation ◽  
Over Time

The paper provides a review of existing libraries and methods of modeling dynamic systems with interval parameters. Available software libraries AWA, VNODELP, COZY Infinity, RiOT, FlowStar, as well as the author’s adaptive interpolation algorithm are considered. The traditional software for interval analysis gives guaranteed estimates of solutions, however, over time, these estimates become extremely significantly overstated. Due to the use of a fundamentally different approach to constructing solutions, the adaptive interpolation algorithm is not subject to the accumulation of errors, determines the boundaries of solutions with controlled accuracy, and works much faster than analogues.

Video image scaling technology based on adaptive interpolation algorithm and TTS FPGA implementation

2021 ◽  
Vol 76 ◽  
pp. 103516
Author(s):  
Guangyu Liu ◽  
Bao Zhou ◽  
Yi Huang ◽  
Longfei Wang ◽  
Wei Wang ◽  
...  
Keyword(s):  
Fpga Implementation ◽  
Video Image ◽  
Interpolation Algorithm ◽  
Image Scaling ◽  
Adaptive Interpolation

Research on Look-Ahead Adaptive Interpolation of NURBS Based on de Boor Algorithm

2010 ◽  
Vol 426-427 ◽  
pp. 206-211
Author(s):  
Y.Q. Fan ◽  
Jian Zhong Fu ◽  
W.F. Gan
Keyword(s):  
Linear Equation ◽  
Interpolation Algorithm ◽  
De Boor Algorithm ◽  
Look Ahead ◽  
Adaptive Interpolation ◽  
Non Linear Equation ◽  
Non Linear ◽  
Basic Functions ◽  
Contour Accuracy ◽  
Interpolation Strategy

This paper realizes direct interpolation of NURBS with use of solving the non-linear equation and de Boor algorithm, which improves the efficiency greatly by avoiding computing the derivatives and basic functions; meanwhile, look-ahead adaptive interpolation algorithm (LAIA) adjusts the feedrate according to the curvature to guarantee the contour accuracy, and the new backtracking and re-interpolation strategy makes it more efficient. Reverse interpolation with use of NURBS symmetry is proposed to predict the deceleration point precisely. The algorithm performs very well in experiments, which prove its viability and reliability.

Sign in / Sign up

Export Citation Format

Share Document