| Title:
|
The Collatz-Wielandt quotient for pairs of nonnegative operators (English) |
| Author:
|
Friedland, Shmuel |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
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0862-7940 (print) |
| ISSN:
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1572-9109 (online) |
| Volume:
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65 |
| Issue:
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5 |
| Year:
|
2020 |
| Pages:
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557-597 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we consider two versions of the Collatz-Wielandt quotient for a pair of nonnegative operators $A,B$ that map a given pointed generating cone in the first space into a given pointed generating cone in the second space. If the two spaces and two cones are identical, and $B$ is the identity operator, then one version of this quotient is the spectral radius of $A$. In some applications, as commodity pricing, power control in wireless networks and quantum information theory, one needs to deal with the Collatz-Wielandt quotient for two nonnegative operators. In this paper we treat the two important cases: a pair of rectangular nonnegative matrices and a pair of completely positive operators. We give a characterization of minimal optimal solutions and polynomially computable bounds on the Collatz-Wielandt quotient. (English) |
| Keyword:
|
Perron-Frobenius theory |
| Keyword:
|
Collatz-Wielandt quotient |
| Keyword:
|
completely positive operator |
| Keyword:
|
commodity pricing |
| Keyword:
|
wireless network |
| Keyword:
|
quantum information theory |
| MSC:
|
15A22 |
| MSC:
|
15A45 |
| MSC:
|
15B48 |
| MSC:
|
15B57 |
| MSC:
|
94A40 |
| idZBL:
|
07285946 |
| idMR:
|
MR4160782 |
| DOI:
|
10.21136/AM.2020.0260-19 |
| . |
| Date available:
|
2020-09-23T13:48:02Z |
| Last updated:
|
2022-11-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148366 |
| . |
| Reference:
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