Results 1 to 10 of about 647,233 (369)
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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Trace inequalities for positive definite matrix power products [PDF]
Linear Algebra and its Applications, 1990 AbstractAn elementary proof is given for the best possible upper and lower bonds of tr(AB)n for Hermitian positive semidefinite N × N matrices A and B.
P. J. Bushell, G. B. Trustrum
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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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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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The positive definite matrix completion problem
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie, 2015 The positive definite matrix completion problem. This study considers under which conditions a partial Hermitian matrix admits a positive definite completion. The answer is closely related to the underlying graph of the matrix.
E. M. Klem
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Notes on the Hermitian Positive Definite Solutions of a Matrix Equation [PDF]
Journal of Applied Mathematics, 2014 The nonlinear matrix equation, X-∑i=1mAi*XδiAi=Q, with -1 ...
Jing Li, Yuhai Zhang
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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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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,
D. O’Leary, G. Stewart, J. Vandergraft
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A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix
, 1986 This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction.
Whitney K. Newey, Kenneth D. West
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Approximating the inverse of a symmetric positive definite matrix
Linear Algebra and its Applications, 1998 Abstract It is shown for an n × n symmetric positive definite matrix T = ( t i , j with negative off-diagonal elements, positive row sums and satisfying certain bounding conditions that its inverse is well approximated, uniformly to order l/ n 2 , by a matrix S = ( s i , j ), where s i , j = δ i , j / t i , j + 1/ t..
Gordon Simons, Yi‐Ching Yao
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