Approximating the inverse of a symmetric positive definite matrix
Linear Algebra and its Applications, 1998 Abstract It is shown for an n × n symmetric positive definite matrix T = ( t i , j with negative off-diagonal elements, positive row sums and satisfying certain bounding conditions that its inverse is well approximated, uniformly to order l/ n 2 , by a matrix S = ( s i , j ), where s i , j = δ i , j / t i , j + 1/ t..
Gordon Simons, Yi‐Ching Yao
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Minimizing the condition number of a positive definite matrix by completion [PDF]
Numerische Mathematik, 1994 Let \(W = W(X)\) denote an Hermitian matrix with blocks \(W_{ij}\), \(i = 1,2\). Three of the four blocks are given, viz. \(W_{11} = A\), an Hermitian positive definite \(n \times n\) matrix and \(W_{21} = W_{12}^ H = B\), a \(p \times n\) matrix. The problem is to complete the matrix with \(W_{22} = X\), a \(p \times p\) matrix such that \(\kappa (W)\)
L. Elsner, C. He, Volker Mehrmann
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Symmetric Positive Semi-Definite Fourier Estimator of Spot Covariance Matrix with High Frequency Data [PDF]
RisksThis paper proposes a nonparametric estimator of the spot volatility matrix with high-frequency data. Our newly proposed Positive Definite Fourier (PDF) estimator produces symmetric positive semi-definite estimates and is consistent with a suitable ...
Jiro Akahori +5 more
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Some inequalities for the square root of a positive definite matrix
Linear Algebra and its Applications, 1968 Richard Bellman
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Establishing the Positive Definiteness of the Sample Covariance Matrix [PDF]
The Annals of Mathematical Statistics, 1970 Richard L. Dykstra
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A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix
, 1986 Whitney K. Newey, Kenneth D. West
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Positive definite solution of non-linear matrix equations through fixed point technique
AIMS Mathematics, 2022 The goal of this study is to solve a non-linear matrix equation of the form $ \mathcal{X} = \mathcal{Q} + \sum\limits_{i = 1}^{m} \mathcal{B}_{i}^{*}\mathcal{G} (\mathcal{X})\mathcal{B}_{i} $, where $ \mathcal{Q} $ is a Hermitian positive definite ...
Sourav Shil, Hemant Kumar Nashine
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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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