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Preserving Positive Definiteness in Hierarchically Semiseparable Matrix Approximations
SIAM Journal on Matrix Analysis and Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xin Xing, Edmond Chow
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Integral representation of invariant positive-definite matrix kernels
Ukrainian Mathematical Journal, 1970zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Samoĭlenko, Yu. S., Korsunskiĭ, L. M.
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Multisplitting of a Symmetric Positive Definite Matrix
SIAM Journal on Matrix Analysis and Applications, 1990The 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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Practical criteria for positive-definite matrix, M-matrix and Hurwitz matrix
Applied Mathematics and Computation, 2007A 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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Identification of a Positive Definite Mass Matrix
Journal of Vibration and Acoustics, 1988In system identification it is important that any a priori information about the system is utilized in the processing of measured data. Structural vibration problems can be modelled in terms of mass, stiffness, and damping and it is usually the case that the mass matrix is positive definite.
John E. Mottershead +2 more
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Conditionally Positive Definite Matrix Valued Kernels on Euclidean Spaces
Constructive Approximation, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guella, J. C., Menegatto, V. A.
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On positive definite solution of a nonlinear matrix equation
Numerical Linear Algebra with Applications, 2006AbstractIn 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 &
Peng, Zhen-yun, El-Sayed, Salah M.
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