Results 1 to 10 of about 43,499 (308)
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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Positive-Definite Sparse Precision Matrix Estimation
Advances in Pure Mathematics, 2017 The positive-definiteness and sparsity are the most important property of high-dimensional precision matrices. To better achieve those property, this paper uses a sparse lasso penalized D-trace loss under the positive-definiteness constraint to estimate high-dimensional precision matrices.
Lin Xia +3 more
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Positive Definite Solutions of the Matrix Equation Xr-∑i=1mAi∗X-δiAi=I [PDF]
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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On the Positive Definite Solutions of a Nonlinear Matrix Equation [PDF]
Journal of Applied Mathematics, 2013 The positive definite solutions of the nonlinear matrix equation are discussed. A necessary and sufficient condition for the existence of positive definite solutions for this equation is derived.
Panpan Liu, Shugong Zhang, Qingchun Li
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An Algorithm for Computing Geometric Mean of Two Hermitian Positive Definite Matrices via Matrix Sign [PDF]
Abstract and Applied Analysis, 2014 Using the relation between a principal matrix square root and its inverse with the geometric mean, we present a fast algorithm for computing the geometric mean of two Hermitian positive definite matrices.
F. Soleymani +3 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.
Zahrasadat Mousavi +2 more
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On Positive Definite Solutions Of Quaternionic Matrix Equations
, 2010 The real representation of the quaternionic matrix is definited and studied. The relations between the positive (semi)define quaternionic matrix and its real representation matrix are presented. By means of the real representation, the relation between the positive (semi)definite solutions of quaternionic matrix equations and those of corresponding ...
Ming-hui Wang
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Spreadsheets in Education, 2010 This study considers, from a pedagogic perspective, a crucial requirement for the covariance matrix of security returns in mean-variance portfolio analysis.
Clarence C. Y. Kwan
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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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mbend: an R package for bending non-positive-definite symmetric matrices to positive-definite
BMC Genetics, 2020 Background R package mbend was developed for bending symmetric non-positive-definite matrices to positive-definite (PD). Bending is a procedure of transforming non-PD matrices to PD.
Mohammad Ali Nilforooshan
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