Between moving least-squares and moving least- $$\ell _1$$ ℓ 1
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0522-0 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0522-0 | ||
| 100 | 1 | |a Levin |D David |u School of Mathematical Sciences, Tel-Aviv University, 69978, Tel Aviv, Israel |4 aut | |
| 245 | 1 | 0 | |a Between moving least-squares and moving least- $$\ell _1$$ ℓ 1 |h [Elektronische Daten] |c [David Levin] |
| 520 | 3 | |a Given function values at scattered points in $${\mathbb {R}}^d$$ R d , possibly with noise, one of the ways of generating approximation to the function is by the method of moving least-squares (MLS). The method consists of computing local polynomials which approximate the data in a locally weighted least-squares sense. The resulting approximation is smooth, and is well approximating if the underlying function is smooth. Yet, as any least-squares based method it is quite sensitive to outliers in the data. It is well known that least- $$\ell _1$$ ℓ 1 approximations are not sensitive to outliers. However, due to the nature of the $$\ell _1$$ ℓ 1 norm, using it in the framework of a "moving” approximation will not give a smooth, or even a continuous approximation. This paper suggests an error measure which is between the $$\ell _1$$ ℓ 1 and the $$\ell _2$$ ℓ 2 norms, with the advantages of both. Namely, yielding smooth approximations which are not too sensitive to outliers. A fast iterative method for computing the approximation is demonstrated and analyzed. It is shown that for a scattered data taken from a smooth function, with few outliers, the new approximation gives an $$O(h)$$ O ( h ) approximation error to the function. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Moving least-squares |2 nationallicence | |
| 690 | 7 | |a Outliers |2 nationallicence | |
| 690 | 7 | |a Multivariate approximation |2 nationallicence | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/3(2015-09-01), 781-796 |x 0006-3835 |q 55:3<781 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0522-0 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0522-0 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Levin |D David |u School of Mathematical Sciences, Tel-Aviv University, 69978, Tel Aviv, Israel |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/3(2015-09-01), 781-796 |x 0006-3835 |q 55:3<781 |1 2015 |2 55 |o 10543 | ||