Algorithms for positive semidefinite factorization
نویسندگان
چکیده
منابع مشابه
Algorithms for Positive Semidefinite Factorization
This paper considers the problem of positive semidefinite factorization (PSD factorization), a generalization of exact nonnegative matrix factorization. Given an m-by-n nonnegative matrix X and an integer k, the PSD factorization problem consists in finding, if possible, symmetric k-by-k positive semidefinite matrices {A, ..., A} and {B, ..., B} such that Xi,j = trace(AB) for i = 1, ...,m, and ...
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Let A be a matrix with nonnegative real entries. The PSD rank of A is the smallest integer k for which there exist k × k real PSD matrices B1, . . . , Bm, C1, . . . , Cn satisfying A(i|j) = tr(BiCj) for all i, j. This paper determines the computational complexity status of the PSD rank. Namely, we show that the problem of computing this function is polynomial-time equivalent to the existential ...
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Incomplete Cholesky factorizations have long been important as preconditioners for use in solving largescale symmetric positive-definite linear systems. In this paper, we focus on the relationship between two important positive semidefinite modification schemes that were introduced to avoid factorization breakdown, namely the approach of Jennings and Malik and that of Tismenetsky. We present a ...
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ژورنال
عنوان ژورنال: Computational Optimization and Applications
سال: 2018
ISSN: 0926-6003,1573-2894
DOI: 10.1007/s10589-018-9998-x