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Numerical Evaluation of Gaussian Mixture Entropy. [PDF]

Entropy (Basel)
Joudeh B, Škorić B.
europepmc   +1 more source

Observer effect modulates classification in a quantum epistemic framework. [PDF]

Sci Rep
Hoorn JF, Ho JKW.
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On the existence of a positive definite solution of the matrix equation

International Journal of Computer Mathematics, 2001
In this paper, an efficient and numerically stable algorithm for computing the positive definite solution of the nonlinear equation is proposed. Some properties of the solution are discussed as well as the sufficient conditions for the existence are obtained.
Mohamed Ramadan, Salah M El-Sayed
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Computing the Extremal Positive Definite Solutions of a Matrix Equation

SIAM Journal of Scientific Computing, 1996
An implementation of a well-known algorithm is proposed for finding extremal positive definite solutions of the matrix equation \(X+A^*X^{-1}A=I\). The convergence rate is analyzed. Then a new algorithm is presented. This algorithm avoids matrix inversions.
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On positive definite solution of a nonlinear matrix equation

Numerical Linear Algebra with Applications, 2006
AbstractIn this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equationX+A*X−αA=Qwith α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rates of convergence of the considered methods are obtained. Copyright © 2006 John Wiley &
Zhen-Yun Peng, Salah M. El-Sayed
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Multisplitting of a Symmetric Positive Definite Matrix

SIAM Journal on Matrix Analysis and Applications, 1990
The author considers parallel iterative methods for systems of linear equations \(Au=d\), \(A=A^*>0\). If \(A=B_ k-C_ k\), \(k=1,...,K\) are given splittings of the matrix A then the iterative methods can be written in the form \(u^{n+1}=\sum_{k}D_ kB_ k^{-1}C_ ku^ n+\sum_{k}D_ kB_ k^{-1}d\) where \(D_ k\geq 0\) are diagonal matrices and \(\sum_{k}D_ k=
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The Cicchetti–Allison weighting matrix is positive definite

Computational Statistics & Data Analysis, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Triangularization of a positive definite matrix on a parallel computer

Journal of Parallel and Distributed Computing, 1986
Abstract The problem of computing the triangular factors of a square, real, symmetric, and positive definite matrix by using the facilities of a multiprocessor MIMD-type computer is considered. The parallel algorithms based on Cholesky decomposition and Gaussian elimination are derived and analyzed in terms of their speedup and efficiency, when the ...
Swarn P. Kumar, Janusz S. Kowalik
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Preserving Positive Definiteness in Hierarchically Semiseparable Matrix Approximations

SIAM Journal on Matrix Analysis and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Xing, Edmond Chow
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Practical criteria for positive-definite matrix, M-matrix and Hurwitz matrix

Applied Mathematics and Computation, 2007
A new simple criterion is presented to verify if a matrix is positive definite, an \(M\)-matrix, or a Hurwitz matrix. It is based on the Gauss row elimination using inner and sign-preserving row operations. The computation of only one determinant is necessary.
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