Article information
2017 , Volume 22, ¹ 2, p.50-58
Kreinovich V., Neumaier A.
For piecewise smooth signals, l 1 - method is the best among l p - methods: an interval-based justification of an empirical fact
Traditional engineering techniques often use the Least Squares Method (i. e., in mathematical terms, minimization of the 𝑙 2 -norm) to process data. It is known that in many real-life situations, 𝑙 𝑝 -methods with 𝑝 ≠2 lead to better results, and different values of 𝑝 are optimal in different practical cases. In particular, when we need to reconstruct a piecewise smooth signal, the empirically optimal value of 𝑝 is close to 1. In this paper, we provide a new theoretical explanation for this empirical fact based on ideas and results from interval analysis.
[full text] Keywords: piecewise smooth signal, l 1- method, interval uncertainty
Author(s): Kreinovich Vladik Professor Position: Professor Office: University of Texas of El Paso Address: 79968, USA, El Paso, 500, W. University
Phone Office: (915) 747-6951 E-mail: vladik@utep.edu Neumaier Arnold Professor Position: Professor Office: University of Vienna Address: Austria, Vienna, A-1090, Vienna, 500, W. University
Phone Office: (431) 4277 50661 E-mail: Arnold.Neumaier@univie.ac.at
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Bibliography link: Kreinovich V., Neumaier A. For piecewise smooth signals, l 1 - method is the best among l p - methods: an interval-based justification of an empirical fact // Computational technologies. 2017. V. 22. ¹ 2. P. 50-58
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