Factorization of cp-rank-3 completely positive matrices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00463394" target="_blank" >RIV/67985840:_____/16:00463394 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10587-016-0303-9" target="_blank" >http://dx.doi.org/10.1007/s10587-016-0303-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10587-016-0303-9" target="_blank" >10.1007/s10587-016-0303-9</a>

Result language
angličtina
Original language name
Factorization of cp-rank-3 completely positive matrices
Original language description
A symmetric positive semi-definite matrix A is called completely positive if there exists a matrix B with nonnegative entries such that A = BB⊤. If B is such a matrix with a minimal number p of columns, then p is called the cp-rank of A. In this paper we develop a finite and exact algorithm to factorize any matrix A of cp-rank 3. Failure of this algorithm implies that A does not have cp-rank 3. Our motivation stems from the question if there exist three nonnegative polynomials of degree at most four that vanish at the boundary of an interval and are orthonormal with respect to a certain inner product.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA14-02067S" target="_blank" >GA14-02067S: Advanced methods for flow-field analysis</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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