Criteria of the k-singularity and division of 1-singular systems
The concept of the k -singularity of systems of points in ℝ m space with l 1 metrics is studied. A system of q points is k -singular if and only if the dimensionality of the linear space of polynomials with powers no higher than the k of the columns of the matrix of pair-wise distances (element-wise...
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| Vydáno v: | Moscow University computational mathematics and cybernetics Ročník 34; číslo 4; s. 164 - 171 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Heidelberg
Allerton Press, Inc
01.12.2010
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| Témata: | |
| ISSN: | 0278-6419, 1934-8428 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | The concept of the
k
-singularity of systems of points in ℝ
m
space with
l
1
metrics is studied. A system of
q
points is
k
-singular if and only if the dimensionality of the linear space of polynomials with powers no higher than the
k
of the columns of the matrix of pair-wise distances (element-wise multiplication) is strictly less than
q
. An algebraic criterion of
k
-singularity is obtained. The problem of dividing a system of points into subsystems that are not 1-singular is considered. An estimate of the minimum number of such subsystems is obtained. |
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| ISSN: | 0278-6419 1934-8428 |
| DOI: | 10.3103/S0278641910040035 |