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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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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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Rotation-based metric on the Riemannian manifold of SPD matrices with applications to source data selection for brain-computer interface transfer learning [PDF]
Frontiers in Human NeuroscienceThis paper introduces the pole ratio metric and presents a sphere-based view of symmetric positive-definite matrix rotations on the Riemannian manifold of symmetric positive-definite matrices equipped with the affine-invariant Riemannian metric. The pole
Frida Heskebeck +2 more
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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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Positive Definiteness of Symmetric Rank 1 (H-Version) Update for Unconstrained Optimization
مجلة بغداد للعلوم, 2022 Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of Hessian matrix (second derivative of the objective function).
Saad Shakir Mahmood +2 more
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ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS
Ural Mathematical Journal, 2023 Let \(\mathbb{C}^{m\times m}\) be the set of all \(m\times m\) matrices whose entries are in \(\mathbb{C},\) the set of complex numbers. Then \(P(z):=\sum\limits_{j=0}^nA_jz^j,\) \(A_j\in \mathbb{C}^{m\times m},\) \(0\leq j\leq n\) is called a matrix ...
Zahid Bashir Monga, Wali Mohammad Shah
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Mathematics, 2022 A non-iterative method for the difference of means is presented to calculate the log-Euclidean distance between a symmetric positive-definite matrix and the mean matrix on the Lie group of symmetric positive-definite matrices.
Xiaomin Duan +3 more
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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.
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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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مجلة بغداد للعلوم, 2020 The study presents the modification of the Broyden-Flecher-Goldfarb-Shanno (BFGS) update (H-Version) based on the determinant property of inverse of Hessian matrix (second derivative of the objective function), via updating of the vector s ( the ...
Saad Shakir Mahmood
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