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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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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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A note on fixed point method and linear complementarity problem
Journal of Numerical Analysis and Approximation Theory, 2023 In this article, we present a general form of the fixed point method for processing the large and sparse linear complementarity problem, as well as a general condition for the method's convergence when the system matrix is a \(P\)-matrix and some ...
Bharat Kumar, Deepmala, Arup K Das
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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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Positive definite estimation of large covariance matrix using generalized nonconvex penalties
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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