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mbend: an R package for bending non-positive-definite symmetric matrices to positive-definite [PDF]
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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Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices
Mathematics, 2016 We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X )
Jean-Paul Chehab, Marcos Raydan
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Strictly Hermitian Positive Definite Functions [PDF]
Journal d'Analyse Mathématique, 2004 Let H be any complex inner product space with inner product . We say that f : C -->C is Hermitian positive definite on H if the matrix $$(f())_{r,s=1}^n \eqno(*)$$ is Hermitian positive definite for all choice of z^1,...,z^n in H, all n.
Pinkus, Allan
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A Note on n-Divisible Positive Definite Functions
Journal of Mathematics, 2022 Let PDℝ be the family of continuous positive definite functions on ℝ. For an integer n>1, a f∈PDℝ is called n-divisible if there is g∈PDℝ such that gn=f. Some properties of infinite-divisible and n-divisible functions may differ in essence.
Saulius Norvidas
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On functional reproducing kernels
Open Mathematics, 2023 We show that even if a Hilbert space does not admit a reproducing kernel, there could still be a kernel function that realizes the Riesz representation map.
Zhou Weiqi
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Stable positive definite functions [PDF]
Transactions of the American Mathematical Society, 1975 This paper investigates the stability of positive definite functions on locally compact groups under one parameter groups of automorphisms. As an application of this it is shown that the only probability distributions on R n {R^n} which are stable under the full automorphism group GL
Parthasarathy, K. R., Schmidt, K.
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Ordering positive definite matrices [PDF]
Information Geometry, 2018 We introduce new partial orders on the set Sn+$$S^+_n$$ of positive definite matrices of dimension n derived from the affine-invariant geometry of Sn+$$S^+_n$$. The orders are induced by affine-invariant cone fields, which arise naturally from a local analysis of the orders that are compatible with the homogeneous geometry of Sn+$$S^+_n$$ defined by ...
Cyrus Mostajeran, Rodolphe Sepulchre
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Positive definite measures [PDF]
Proceedings of the American Mathematical Society, 1963 In this paper we prove two theorems relating positive definite measures to induced representations. The first shows how the injection of a positive definite measure on a topological group H into a containing locally compact group G in which H is closed gives rise to induced representations.
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Positive Inductive-Recursive Definitions [PDF]
Logical Methods in Computer Science, 2013 A new theory of data types which allows for the definition of types as initial algebras of certain functors Fam(C) -> Fam(C) is presented. This theory, which we call positive inductive-recursive definitions, is a generalisation of Dybjer and Setzer's theory of inductive-recursive definitions within which C had to be discrete -- our work can ...
Ghani, Neil +2 more
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Journal of Inequalities and Applications, 2016 We consider two nonlinear matrix equations X r ± ∑ i = 1 m A i ∗ X δ i A i = I $X^{r} \pm \sum_{i = 1}^{m} A_{i}^{*}X^{\delta_{i}}A_{i} = I$ , where − 1 < δ i < 0 $- 1 < \delta_{i} < 0$ , and r, m are positive integers. For the first equation (plus case),
Abdel-Shakoor M Sarhan +1 more
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