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Approximation-Degree-Based Interpolation: A New Interpolation Method

Submit Time: 2019-12-29
Author: 廉师友 1 ;
Institute: 1.西安石油大学;

Abstracts

This paper introduces the measure of approximate-degree and the concept of approximate-degree function between numerical values, thus developing a new interpolation method —— approximation-degree-based interpolation, i.e., AD interpolation. One-dimensional AD interpolation is done directly by using correlative interpolation formulas; n(n>1)-dimensional AD interpolation is firstly separated into n parallel one-dimensional AD interpolation computations to do respectively, and then got results are synthesized by Sum-Times-Difference formula into a value as the result value of the n-dimensional interpolation. If the parallel processing is used, the efficiency of n-dimensional AD interpolation is almost the same as that of the one-dimensional AD interpolation. Thus it starts a feasible and convenient approach and provides an effective method for high-dimensional interpolations. Furthermore, if AD interpolation is introduced into machine learning, a new instance-based learning method is expected to be realized.
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From: 廉师友
DOI:10.12074/202001.00045
Recommended references: 廉师友.(2019).Approximation-Degree-Based Interpolation: A New Interpolation Method.[ChinaXiv:202001.00045] (Click&Copy)
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[V1] 2019-12-29 10:47:56 chinaXiv:202001.00045V1 Download
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