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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
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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.
Tropp, Joel A.
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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
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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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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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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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Fundamental Solution of Elliptic Equation with Positive Definite Matrix Coefficient
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2018 In this paper, we study the fundamental solution of elliptic equations with real constant coefficients where is a positive definite matrix. We obtained by searching the radial solution so that we solved the equation into ordinary differential equations.
Khoirunisa Khoirunisa, Corina Karim
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