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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
doaj   +4 more sources

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 Neuroscience
This 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, Bo Bernhardsson, Carolina Bergeling   +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
doaj   +1 more source

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, Jaafer Hmood Eidi, Jinan Adel Jasem   +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
doaj   +1 more source

A Non-Iterative Method for the Difference of Means on the Lie Group of Symmetric Positive-Definite Matrices

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, Xueting Ji, Huafei Sun, Hao Guo   +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., Stewart, G. W., Vandergraft, James S.   +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.
openaire   +1 more source

Modified BFGS Update (H-Version) Based on the Determinant Property of Inverse of Hessian Matrix for Unconstrained Optimization

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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