ensures that is positive definite. Denoting the
UNBOUNDED POSITIVE DEFINITE FUNCTIONS
... / positive definite for F, where F is a set of functions on R, if the integral in (2) exists and is non-negative for every (p G ...is positive definite for C c is the Fourier-Stieltjes ...
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Complementarity Problems And Positive Definite Matrices
... of positive definite and positive semidefinite matrices is one of the most frequently encountered matrix classes both in theory and ...by positive semidefinite matrices have some interesting ...
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Design of Positive-Definite Quaternion Kernels
... are positive definite in the real or complex fields, cannot be straightforwardly extended to the quaternion ring ...their positive definiteness relies upon the assumption of commutativity, thus ...
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POSITIVE DEFINITE SOLUTION OF NONLINEAR MATRIX EQUATIONS
... with s 0, 0 t i 1 and studied the existence and the uniqueness of the HPD solution. In this paper, we discuss X s A X * t 1 A B X * t 2 B I with s t t , , 1 2 0 . We propose necessary and sufficient ...
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On The Frobenius Condition Number of Positive Definite Matrices
... be positive semidefinite or nonnegative definite, written as A ≥ 0, if see, ...called positive definite, symbolized A > 0, if the strict inequality in ...be positive definite is ...
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Positive Definite Sparse Precision Matrix Estimation
... considered a constrained 1 minimization estimator for estimating sparse precision matrices. However, this methods mentioned are not always achieve a positive-definiteness. To overcome the difficulty (ii), one ...
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Factorizations and geometric means of positive definite matrices
... geodesically convex subsets and a Hadamard metric structure on P m . An explicit formula for the corresponding metric midpoint op- eration is presented in terms of the geometric and spectral geometric means and show that ...
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2 Positive definite solution of Eqs. (1.1) and (1.2)
... P i=1 (A ∗ i XA i ) δ i , (0 < |δ i | < 1) always have a unique positive definite solution. Iterative methods are proposed to compute the unique positive definite solution. We show that ...
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CiteSeerX — APPROXIMATING THE INVERSE OF A SYMMETRIC POSITIVE DEFINITE MATRIX
... SYMMETRIC POSITIVE DEFINITE MATRIX Gordon Simons and Yi-Ching Yao Abstract It is shown for an n n symmetric positive de nite matrix T = ( t i;j ) with negative o -diagonal elements, positive ...
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CiteSeerX — Strictly Positive Definite Functions On A Compact Group
... for ompa
t groups. The purpose of this note is to provide a rapid proof of a relatively new result of S
hreiner, [S℄, on
erning stri
tly positive de nite fun
tions on a sphere in an eu
lidean spa
e. It is our ...
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A note on the Frobenius conditional number with positive definite matrices
... is positive definite, then any eigenvalue of A is positive real ...all positive real ...are positive real ...both positive definite. It is obvious that M -1 and N -1 are ...
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On some trace inequalities for positive definite Hermitian matrices
... matrix; positive definite; trace inequality 1 Introduction In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with com- plex entries that is equal to its own conjugate ...
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Positive Definite Operator Valued Kernels and Integral Representations
... atomic, positive, operator-valued measure E , with the property that for every n Z p with n i s i ,1 i p , the n th moment of E coincides with the n th term s n of the sequence, is ...some ...
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Positive Definite Matrices: Compression, Decomposition, Eigensolver, and Concentration
... The computation of eigenpairs for large and sparse matrices, particularly for positive semidefinite matrices (PSD) matrices, is one of the most fundamental tasks in many scientific applications. For example, the ...
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Symmetric and Positive Definite Broyden Update for Unconstrained Optimization
... Conclusion: In this paper, the Broyden update is modified to guarantee the symmetric and positively definite properties and the so called symmetric positive definite Broyden update. The convergence ...
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Exploration of Balanced Metrics on Symmetric Positive Definite Matrices
... Symmetric Positive Definite Matrices Yann Thanwerdas and Xavier Pennec Universit´e Cˆ ote d’Azur, Inria, Epione, France ...Symmetric Positive Definite (SPD) matrices have been used in many ...
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Convergence of a Positive-Definite Scaled Symmetric Rank One Method
... non-positive definite H k with a positive multiple of the identity ...are positive-definite and bounded asymptotically, which are the actual conditions given by ...
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Differentiable positive definite kernels on two-point homogeneous spaces
... Juiz de Fora, MG, Brasil, 5 Partially supported by CNPq/Brasil and INCTMAT/Brasil. † [email protected], ‡ [email protected], § [email protected] Abstract This work deals with existence of solutions for a class ...
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On the HSS iteration methods for positive definite Toeplitz linear systems
... not positive definite, then the HSS 2 iteration method diverges since H is not a positive definite matrix; ˜ while H is positive definite, then the HSS 1 iteration method ...
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Nearly optimal fast preconditioning of symmetric positive definite matrices
... Project-Team HiePACS Research Report n° 8984 — November 2016 — 35 pages Abstract: We consider the hierarchical off-diagonal low-rank preconditioning of symmetric positive definite matrices arising from ...
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