Loading...
Please wait, while we are loading the content...
Similar Documents
Lp Linear Discrepancy of Totally Unimodular Matrices ∗
| Content Provider | Semantic Scholar |
|---|---|
| Author | Doerr, Benjamin |
| Copyright Year | 2006 |
| Abstract | Let p ∈ [1,∞[ and cp = maxa∈[0,1]((1 − a)ap + a(1 − a)p)1/p. We prove that the known upper bound lindiscp(A) ≤ cp for the Lp linear discrepancy of a totally unimodular matrix A is asymptotically sharp, i.e., sup A lindiscp(A) = cp. We estimate cp = p p+1 ( 1 p+1 )1/p (1+εp) for some εp ∈ [0, 2−p+2], hence cp = 1− ln p p (1+ o(1)). We also show that an improvement for smaller matrices as in the case of L∞ linear discrepancy cannot be expected. For any p ∈ N we give a totally unimodular (p + 1)× p matrix having Lp linear discrepancy greater than p p+1 ( 1 p+1 )1/p . ∗key words: linear discrepancy, totally unimodular matrix, rounding, halftoning. AMS classification: 11K38. †Max–Planck–Institut für Informatik, Saarbrücken, Germany. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://people.mpi-inf.mpg.de/~doerr/papers/lplindtu.pdf |
| Alternate Webpage(s) | https://people.mpi-inf.mpg.de/~doerr/papers/lplindtu.pdf |
| Alternate Webpage(s) | http://www.mpi-inf.mpg.de/~doerr/papers/lplindtu.pdf |
| Alternate Webpage(s) | http://www.mpi-sb.mpg.de/~doerr/papers/lplindtu.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | ABLEPHARON-MACROSTOMIA SYNDROME Discrepancy function Rounding Unimodular polynomial matrix newton |
| Content Type | Text |
| Resource Type | Article |
