Results 1 to 10 of about 564,115 (361)
Integer Factorization of a Positive-Definite Matrix [PDF]
SIAM Journal on Discrete Mathematics, 2015 This paper establishes that every positive-definite matrix can be written as a positive linear combination of outer products of integer-valued vectors whose entries are bounded by the geometric mean of the condition number and the dimension of the matrix.
J. Tropp
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Positive definite estimation of large covariance matrix using generalized nonconvex penalties [PDF]
IEEE Access, 2016 This paper addresses the issue of large covariance matrix estimation in a high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed.
Fei Wen +3 more
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Estimating the largest eigenvalue of a positive definite matrix [PDF]
Mathematics of Computation, 1979 The power method for computing the dominant eigenvector of a positive definite matrix will converge slowly when the dominant eigenvalue is poorly separated from the next largest eigenvalue. In this note it is shown that in spite of this slow convergence, the Rayleigh quotient will often give a good approximation to the dominant eigenvalue after a very ...
O'Leary, Dianne P. +2 more
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Matrix-valued positive definite kernels given by expansions: strict positive definiteness [PDF]
Mathematical Inequalities & Applications, 2021 Given a nonempty set $\Omega$, the authors consider positive definite matrix-valued kernels $F:\Omega\times\Omega\to M_p(\mathbb{C})$ in the form $$ F(x,y)=\sum_{\alpha\in J}A_\alpha f_\alpha(x,y), \quad x,y\in\Omega, $$ where $J\subset\mathbb{Z}^q$ for some positive integer $q$, each $A_\alpha\in M_p(\mathbb{C})$ is a positive semidefinite matrix ...
Franca, Willian, Menegatto, V. A.
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The positive definite matrix completion problem
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie, 2015 No abstract ...
E. M. Klem
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On The Positive Definite Solutions Of Nonlinear Matrix Equation
, 2013 In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δi are discussed. An algorithm that avoids matrix inversion with the case -1<-δi<0 is proposed.
Baoguang, Tian +2 more
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Positive Definite Solutions of the Matrix Equation Xr-∑i=1mAi∗X-δiAi=I
Abstract and Applied Analysis, 2015 We investigate the nonlinear matrix equation Xr-∑i=1mAi∗X-δiAi=I, where r is a positive integer and δi∈(0,1], for i=1,2,…,m. We establish necessary and sufficient conditions for the existence of positive definite solutions of this equation.
Asmaa M. Al-Dubiban
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Novel Steganographic Method Based on Hermitian Positive Definite Matrix and Weighted Moore–Penrose Inverses [PDF]
Applied SciencesIn this paper, we describe the concept of a new data-hiding technique for steganography in RGB images where a secret message is embedded in the blue layer of specific bytes.
Selver Pepić +6 more
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Positive definite solutions of certain nonlinear matrix equations [PDF]
Operators and Matrices, 2016 Using appropriate inequalities and some fixed point results, the authors prove the existence of unique positive definite solutions for some nonlinear matrix equations.
Mousavi, Z. +2 more
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Active Positive-Definite Matrix Completion [PDF]
SDM, 2017 Charalampos Mavroforakis +3 more
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