Results 1 to 10 of about 554,064 (360)
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 ...
Tropp, Joel A.
core +10 more sources
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
doaj +4 more sources
Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0) [PDF]
Abstract and Applied Analysis, 2013 The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated.
Jing Li
doaj +4 more sources
On Matrix-Valued Square Integrable Positive Definite Functions [PDF]
Monatshefte für Mathematik, 2015 In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on square integrable positive definite functions to matrix valued square integrable positive definite functions.
He, Hongyu
core +6 more sources
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
doaj +4 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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 ...
G. W. Stewart +2 more
openaire +3 more sources
Notes and counterexamples on positive (semi) definite properties of some matrix products
Ain Shams Engineering Journal, 2018 In the present paper, we give some notes and counterexamples to show that the positive (semi) definite property of the Khatri-Rao and Tracy-Singh products of partitioned matrices are in general incorrect and show also that the matrix triangle inequality ...
Zeyad Al-Zhour
doaj +2 more sources
The positive definite matrix completion problem
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie, 2015 No abstract ...
E. M. Klem
openaire +4 more sources