The Experts below are selected from a list of 105 Experts worldwide ranked by ideXlab platform
W. Eberly - One of the best experts on this subject based on the ideXlab platform.
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SPDP - Efficient parallel Independent Subsets and matrix factorizations
Proceedings of the Third IEEE Symposium on Parallel and Distributed Processing, 1991Co-Authors: W. EberlyAbstract:A parallel algorithm is given for computation of a maximal Linearly Independent Subset of a set of vectors over a field. The algorithm uses polylogarithmic time and uses a number of processors that differs by only a polylog factor from the number required for fast parallel matrix inversion. It is used to produce efficient parallel algorithms for orthogonalizations of arbitrary matrices over real fields, and for P-L-U factorizations of nonsingular matrices over arbitrary fields. These are the first processor-efficient highly parallel algorithms known for these problems. >
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Efficient parallel Independent Subsets and matrix factorizations
Proceedings of the Third IEEE Symposium on Parallel and Distributed Processing, 1991Co-Authors: W. EberlyAbstract:A parallel algorithm is given for computation of a maximal Linearly Independent Subset of a set of vectors over a field. The algorithm uses polylogarithmic time and uses a number of processors that differs by only a polylog factor from the number required for fast parallel matrix inversion. It is used to produce efficient parallel algorithms for orthogonalizations of arbitrary matrices over real fields, and for P-L-U factorizations of nonsingular matrices over arbitrary fields. These are the first processor-efficient highly parallel algorithms known for these problems.
John H. Reif - One of the best experts on this subject based on the ideXlab platform.
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Parallel Output-Sensitive Algorithms for Combinatorial and Linear Algebra Problems
Journal of Computer and System Sciences, 2001Co-Authors: John H. ReifAbstract:This paper gives output-sensitive parallel algorithms whose performance depends on the output size and are significantly more efficient tan previous algorithms for problems with sufficiently small output size. Inputs are n×n matrices over a fixed ground field. Let P(n) and M(n) be the PRAM processor bounds for O(logn) time multiplication of two degree n polynomials, and n×n matrices, respectively. Let T(n) be the time bounds, using M(n) processors, for testing if an n×n matrix is nonsingular, and if so, computing its inverse. We compute the rankR of a matrix in randomized parallel time O(logn+T(R)logR) using nP(n)+M(R) processors (P(n)+RP(R) processors for constant displacement rank matrices, e.g., Toeplitz matrices). We find a maximum Linearly Independent Subset (MLIS) of an n-set of n-dimensional vectors in time O(T(n)logn) using M(n) randomized processors and we also give output-sensitive algorithms for this problem. Applications include output-sensitive algorithms for finding: (i) a size R maximum matching in an n-vertex graph using time O(T(R)logn) and nP(n)/T(R)+RM(R) processors, and (ii) a maximum matching in an n-vertex bipartite graph, with vertex Subsets of sizes n1?n2, using time O(T(n1)logn) and nP(n)/T(n1)+n1M(n1) processors.
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SPAA - Parallel and output sensitive algorithms for combinatorial and linear algebra problems
Proceedings of the fifth annual ACM symposium on Parallel algorithms and architectures - SPAA '93, 1993Co-Authors: Joseph Cheriyan, John H. ReifAbstract:This paper gives output-sensitive parallel algorithms whose performance depends on the output size and are significantly more efficient tan previous algorithms for problems with sufficiently small output size. Inputs are n_n matrices over a fixed ground field. Let P(n) and M(n) be the PRAM processor bounds for O(log n) time multiplication of two degree n polynomials, and n_n matrices, respectively. Let T(n) be the time bounds, using M(n) processors, for testing if an n_n matrix is nonsingular, and if so, computing its inverse. We compute the rank R of a matrix in randomized parallel time O(log n+T(R) log R) using nP(n)+M(R) processors (P(n)+RP(R) processors for constant displacement rank matrices, e.g., Toeplitz matrices). We find a maximum Linearly Independent Subset (MLIS) of an n-set of n-dimensional vectors in time O(T(n) log n) using M(n) randomized processors and we also give output-sensitive algorithms for this problem. Applications include output-sensitive algorithms for finding: (i) a size R maximum matching in an n-vertex graph using time O(T(R) log n) and nP(n) T(R)+RM(R) processors, and (ii) a maximum matching in an n-vertex bipartite graph, with vertex Subsets of sizes n1 n2 , using time O(T(n1) log n) and nP(n) T(n1)+ n1 M(n1) processors. 2001 Academic Press
Ziyun Zhang - One of the best experts on this subject based on the ideXlab platform.
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Probabilistic quantum cloning of a Subset of Linearly dependent states
European Physical Journal D, 2018Co-Authors: Wen Zhang, Yanlin Liao, Ziyun ZhangAbstract:It is well known that a quantum state, secretly chosen from a certain set, can be probabilistically cloned with positive cloning efficiencies if and only if all the states in the set are Linearly Independent. In this paper, we focus on probabilistic quantum cloning of a Subset of Linearly dependent states. We show that a Linearly-Independent Subset of Linearly-dependent quantum states {|Ψ1⟩,|Ψ2⟩,…,|Ψ n ⟩} can be probabilistically cloned if and only if any state in the Subset cannot be expressed as a linear superposition of the other states in the set {|Ψ1⟩,|Ψ2⟩,…,|Ψ n ⟩}. The optimal cloning efficiencies are also investigated.
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Part probabilistic cloning of Linearly dependent states
arXiv: Quantum Physics, 2016Co-Authors: Wen Zhang, Yanlin Liao, Ziyun ZhangAbstract:From Ref. [Phys. Rev. Lett. 80(1998)4999] one knows that the quantum states secretly chosen from a certain set can be probabilistically cloned with positive cloning efficiencies if and only if all the states in the set are Linearly Independent. In this paper, we focus on the probabilistic quantum cloning (PQC) of Linearly dependent states with nonnegative cloning efficiencies. We show that a Linearly Independent Subset of the Linearly dependent quantum states can be probabilistically cloned if and only if any one state in the Subset can not be expressed as the linear superposition of the other states in the set. The optimal possible cloning efficiencies are also investigated.
Alexander Kreuzer - One of the best experts on this subject based on the ideXlab platform.
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Free modules over hjelmslev rings in which not every maximal Linearly Independent Subset is a basis
Journal of Geometry, 1992Co-Authors: Alexander KreuzerAbstract:First it will be shown that every left-noetherian AH-ring is left-artinian. For an AH-ring R every finite Linearly Independent Subset of a free left R-module V can be completed to a basis of V. But a maximal Linearly Independent Subset of a free left R-module V need not be a basis of V. For an H-ring R, every maximal Linearly Independent Subset of a free left R-module V is a basis of V if and only if the H-ring R is left-noetherian or V is finitely generated.
Wen Zhang - One of the best experts on this subject based on the ideXlab platform.
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Probabilistic quantum cloning of a Subset of Linearly dependent states
European Physical Journal D, 2018Co-Authors: Wen Zhang, Yanlin Liao, Ziyun ZhangAbstract:It is well known that a quantum state, secretly chosen from a certain set, can be probabilistically cloned with positive cloning efficiencies if and only if all the states in the set are Linearly Independent. In this paper, we focus on probabilistic quantum cloning of a Subset of Linearly dependent states. We show that a Linearly-Independent Subset of Linearly-dependent quantum states {|Ψ1⟩,|Ψ2⟩,…,|Ψ n ⟩} can be probabilistically cloned if and only if any state in the Subset cannot be expressed as a linear superposition of the other states in the set {|Ψ1⟩,|Ψ2⟩,…,|Ψ n ⟩}. The optimal cloning efficiencies are also investigated.
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Part probabilistic cloning of Linearly dependent states
arXiv: Quantum Physics, 2016Co-Authors: Wen Zhang, Yanlin Liao, Ziyun ZhangAbstract:From Ref. [Phys. Rev. Lett. 80(1998)4999] one knows that the quantum states secretly chosen from a certain set can be probabilistically cloned with positive cloning efficiencies if and only if all the states in the set are Linearly Independent. In this paper, we focus on the probabilistic quantum cloning (PQC) of Linearly dependent states with nonnegative cloning efficiencies. We show that a Linearly Independent Subset of the Linearly dependent quantum states can be probabilistically cloned if and only if any one state in the Subset can not be expressed as the linear superposition of the other states in the set. The optimal possible cloning efficiencies are also investigated.
