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On positive definite solution of nonlinear matrix equations
Linear and Multilinear Algebra, 2017AbstractIn this article, we present a sufficient condition for the existence of a unique positive definite solution of the non-linear matrix equation , where , (the set of all Hermitian positive definite matrices), are non-singular matrices and are order-preserving mappings. We give an example of a non-linear matrix equation of the above form (, A is a
Sk. Monowar Hossein +2 more
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Positive definite solution of a nonlinear matrix equation
Journal of Fixed Point Theory and Applications, 2016The authors use fixed-point theory to present a sufficient condition for the existence of a positive definite solution of the nonlinear matrix equation \(X=Q\pm\sum_{i1}^m A_i^* F(X)A_i\), where \(Q\) is a positive definite matrix, \(A_i\)'s are arbitrary \(n\times n\) matrices and \(F\) is a monotone map from the set of positive definite matrices to ...
Bose, Snehasish +2 more
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The approximate factorization of positive-definite matrix functions
Russian Mathematical Surveys, 1999It is well known that the prediction problem for a stationary process can be reduced to that of factorizing a positive-definite matrix function \(S(t)\) as \(S(t)= \chi^+(t)\cdot(\chi^+(t))^*\), \(|t|= 1\), where \(\chi^+\) is an outer analytic matrix function with entries of Hardy class \(H_2\) and \(^*\) denotes the Hermitian conjugate.
Janashia, G. A. +2 more
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A positive-definite matrix which is not extendible
IEEE Transactions on Acoustics, Speech, and Signal Processing, 1984This note treats the problem of extendibility of a positive-definite matrix. The difference between extendibility and positive- semidefiniteness in multiple dimensions is described. The construction of a positive definite nonextendible correlation matrix is also given.
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Globally convergent Jacobi methods for positive definite matrix pairs
Numerical Algorithms, 2017V. Hari
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Image clustering based on hermetian positive definite matrix and radial Jacobi moments
International Symposium on Computer Vision, 2018A. Hjouji +4 more
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On Projection of a Positive Definite Matrix on a Cone of Nonnegative Definite Toeplitz Matrices
, 2018K. Filipiak +3 more
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The biofilm matrix: multitasking in a shared space
Nature Reviews Microbiology, 2022Hans-Curt Flemming +2 more
exaly
Cubic Algorithm to Compute the Dynkin Type of a Positive Definite Quasi-Cartan Matrix
Fundamenta Informaticae, 2018C. Pérez, M. Abarca, D. Rivera
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