The Experts below are selected from a list of 253740 Experts worldwide ranked by ideXlab platform
Anastasios Zouzias - One of the best experts on this subject based on the ideXlab platform.
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hidden cliques and the certification of the restricted isometry property
IEEE Transactions on Information Theory, 2014Co-Authors: Pascal Koiran, Anastasios ZouziasAbstract:Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing Matrix such as the restricted isometry property. Sensing matrices that satisfy this property with optimal parameters are mainly obtained via probabilistic argu- ments. Deciding whether a Given Matrix satisfies the restricted isometry property is a non-trivial computational problem. In- deed, it is shown in this paper that restricted isometry parameters cannot be approximated in polynomial time within any constant factor under the assumption that the hidden clique problem is hard. Moreover, on the positive side an improvement on the brute- force enumeration algorithm for checking the restricted isometry property is proposed.
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Hidden cliques and the certification of the restricted isometry property
IEEE Transactions on Information Theory, 2014Co-Authors: Pascal Koiran, Anastasios ZouziasAbstract:Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing Matrix such as the restricted isometry property. Sensing matrices that satisfy this property with optimal parameters are mainly obtained via probabilistic arguments. Deciding whether a Given Matrix satisfies the restricted isometry property is a non-trivial computational problem. Indeed, we show in this paper that restricted isometry parameters cannot be approximated in polynomial time within any constant factor under the assumption that the hidden clique problem is hard. Moreover, on the positive side we propose an improvement on the brute-force enumeration algorithm for checking the restricted isometry property.
Pascal Koiran - One of the best experts on this subject based on the ideXlab platform.
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hidden cliques and the certification of the restricted isometry property
IEEE Transactions on Information Theory, 2014Co-Authors: Pascal Koiran, Anastasios ZouziasAbstract:Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing Matrix such as the restricted isometry property. Sensing matrices that satisfy this property with optimal parameters are mainly obtained via probabilistic argu- ments. Deciding whether a Given Matrix satisfies the restricted isometry property is a non-trivial computational problem. In- deed, it is shown in this paper that restricted isometry parameters cannot be approximated in polynomial time within any constant factor under the assumption that the hidden clique problem is hard. Moreover, on the positive side an improvement on the brute- force enumeration algorithm for checking the restricted isometry property is proposed.
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Hidden cliques and the certification of the restricted isometry property
IEEE Transactions on Information Theory, 2014Co-Authors: Pascal Koiran, Anastasios ZouziasAbstract:Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing Matrix such as the restricted isometry property. Sensing matrices that satisfy this property with optimal parameters are mainly obtained via probabilistic arguments. Deciding whether a Given Matrix satisfies the restricted isometry property is a non-trivial computational problem. Indeed, we show in this paper that restricted isometry parameters cannot be approximated in polynomial time within any constant factor under the assumption that the hidden clique problem is hard. Moreover, on the positive side we propose an improvement on the brute-force enumeration algorithm for checking the restricted isometry property.
Boris A Khoruzhenko - One of the best experts on this subject based on the ideXlab platform.
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On Absolute Moments of Characteristic Polynomials of a Certain Class of Complex Random Matrices
Communications in Mathematical Physics, 2007Co-Authors: Yan V Fyodorov, Boris A KhoruzhenkoAbstract:The integer moments of the spectral determinant | det ( zI − W ) |^2 of complex random matrices W are obtained in terms of the characteristic polynomial of the positive-semidefinite Matrix WW ^† for the class of matrices W = AU , where A is a Given Matrix and U is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results are discussed in this context.
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on absolute moments of characteristic polynomials of a certain class of complex random matrices
arXiv: Mathematical Physics, 2006Co-Authors: Yan V Fyodorov, Boris A KhoruzhenkoAbstract:Integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ are obtained in terms of the characteristic polynomial of the Hermitian Matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a Given Matrix and $U$ is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results in this context are discussed.
W U Yousheng - One of the best experts on this subject based on the ideXlab platform.
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least square solutions of inverse problem for symmetric orthogonal anti symmetric matrices
Journal of Gansu Sciences, 2006Co-Authors: W U YoushengAbstract:The least-square solutions of the inverse problem of symmetric orthogonal anti-symmetric matrices is discussed,and the expression of the solution is obtained.In addition,the problem of using symmetric orthogonal anti-symmetric matrices to construct the optimal approximation to a Given Matrix is discussed,the necessary and sufficient conditions about the problem are derived,and the expression of the solution is provided.
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least square solutions of inverse problem for hermitian and generalized skew hamilton matrices
2005Co-Authors: Qian Ailin, W U YoushengAbstract:The least-square solutions of the inverse problem of Hermite and generalized skew-Hamilton matrices is discussed, and an expression of the solution is obtained.In addition, a problem of using Hermite and generalized skew-Hamilton matrices to construct the optimalapproximation to a Given Matrix is discussed, the necessary and sufficient conditions for this problem are derived,and the expression of the solution is Given.
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least square solutions of inverse problem for symmetric and skew anti symmetric matrices
Journal of Xianning Teachers College, 2004Co-Authors: W U YoushengAbstract:The least-square solutions of the inverse problem of symmetric and skew anti-Symmetric matrices is discussed,and expression of the solution is obtained. In addition, the proProblem of using symmetric and skew anti-symmetric matrices to construct the optimalapproximation to a Given Matrix is discussed, the necessary and sufficient conditions about the problem are derived,and the expression of the solution is provided.
Yan V Fyodorov - One of the best experts on this subject based on the ideXlab platform.
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On Absolute Moments of Characteristic Polynomials of a Certain Class of Complex Random Matrices
Communications in Mathematical Physics, 2007Co-Authors: Yan V Fyodorov, Boris A KhoruzhenkoAbstract:The integer moments of the spectral determinant | det ( zI − W ) |^2 of complex random matrices W are obtained in terms of the characteristic polynomial of the positive-semidefinite Matrix WW ^† for the class of matrices W = AU , where A is a Given Matrix and U is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results are discussed in this context.
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on absolute moments of characteristic polynomials of a certain class of complex random matrices
arXiv: Mathematical Physics, 2006Co-Authors: Yan V Fyodorov, Boris A KhoruzhenkoAbstract:Integer moments of the spectral determinant $|\det(zI-W)|^2$ of complex random matrices $W$ are obtained in terms of the characteristic polynomial of the Hermitian Matrix $WW^*$ for the class of matrices $W=AU$ where $A$ is a Given Matrix and $U$ is random unitary. This work is motivated by studies of complex eigenvalues of random matrices and potential applications of the obtained results in this context are discussed.
