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Positive Semidefiniteness and Positive Definiteness of a Linear Parametric Interval Matrix

arXiv.org, 2017
We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters, the matrix is ...
M. Hladík
semanticscholar   +3 more sources

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Verification of Positive Definiteness

BIT Numerical Mathematics, 2006
We present a computational, simple and fast sufficient criterion to verify positive definiteness of a symmetric or Hermitian matrix. The criterion uses only standard floating-point operations in rounding to nearest, it is rigorous, it takes into account all possible computational and rounding errors, and is also valid in the presence of underflow.
S. Rump, S. Rump
semanticscholar   +3 more sources

Conditional positive definiteness in operator theory

Dissertationes Mathematicae, 2020
In this paper we extensively investigate the class of conditionally positive definite operators, namely operators generating conditionally positive definite sequences.
Zenon Jan Jablo'nski, I. Jung, J. Stochel   +2 more
semanticscholar   +1 more source

On the Measurability of Positive Definite and Conditionally Positive Definite Functions [PDF]

Mathematische Nachrichten, 1986
Let f be a positive definite function on a locally compact abelian group G. In this paper we show that measurability of f on an open neighbourhood of the zero implies measurability of f on G. The same result holds for conditionally positive definite functions.
openaire   +1 more source

Preserving Positive Definiteness in Hierarchically Semiseparable Matrix Approximations

SIAM Journal on Matrix Analysis and Applications, 2018
Given a symmetric positive definite (s.p.d.) matrix, two methods are proposed for directly constructing hierarchically semiseparable (HSS) matrix approximations that are guaranteed to be positive d...
Xin Xing, Edmond Chow
semanticscholar   +1 more source

Strict positive definiteness on products of compact two-point homogeneous spaces

, 2016
We present an explicit characterization for the real, continuous, isotropic and strictly positive definite kernels on a product of compact two-point homogeneous spaces, covering almost all possible choices for the spaces.
V. S. Barbosa, V. Menegatto
semanticscholar   +1 more source

Positive Definiteness of Generalized Homogeneous Functions

IFAC Symposium on Nonlinear Control Systems, 2013
Identification of positive definiteness of functions is crucial in control theory. However for generalized homogeneous functions, there does not exist an effective method to identify the positive definiteness.
Hisakazu Nakamura
semanticscholar   +1 more source

Positive definiteness and holomorphy [PDF]

, 1983
Conditions for holomorphic extensions of operator-valued functions in domains D (or complex manifolds) of ℂn are formulated in terms of positive-definiteness of order 3 of certain kernels on D×D.
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Positive Definite Matrices

The American Mathematical Monthly, 1970
(1970). Positive Definite Matrices. The American Mathematical Monthly: Vol. 77, No. 3, pp. 259-264.
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