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Matrix positivity preservers in fixed dimension. I [PDF]
Advances in Mathematics, 2016 A classical theorem of I.J. Schoenberg characterizes functions that preserve positivity when applied entrywise to positive semidefinite matrices of arbitrary size. Obtaining similar characterizations in fixed dimension is intricate. In this note, we provide a solution to this problem in the polynomial case.
Alexander Belton +3 more
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Positivity Preserving Multiapproximation
American Journal of Scientific and Industrial Research, 2012 We show that the degree of copositive multipolynomial approximation to a function which changes signs finitely many times in , can be estimated by ...
Eman Bhaya, Mayada Ali
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Positivity of flux vector splitting schemes [PDF]
, 1999 Over the last ten years, robustness of schemes has raised an increasing interest among the CFD community. One mathematical aspect of scheme robustness is the positivity preserving property.
Moschetta, Jean-Marc +2 more
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Positivity preservation of implicit discretizations of the advection equation
CoRR, 2021 Preprint: Weierstraß-Institut für Angewandte Analysis und Stochastik, vol ...
Yiannis Hadjimichael +2 more
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A positivity-preserving unigrid method for elliptic PDEs
CoRR, 2023 While constraints arise naturally in many physical models, their treatment in mathematical and numerical models varies widely, depending on the nature of the constraint and the availability of simulation tools to enforce it. In this paper, we consider the solution of discretized PDE models that have a natural constraint on the positivity (or non ...
Ronald D. Haynes +2 more
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\({K}\)-Positivity Preservers and Their Generators
SIAM Journal on Applied Algebra and GeometryWe study $K$-positivity preservers with given closed $K\subseteq\mathbb{R}^n$, i.e., linear maps $T:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}[x_1,\dots,x_n]$ such that $T\mathrm{Pos}(K)\subseteq\mathrm{Pos}(K)$ holds, and their generators $A:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}[x_1,\dots,x_n]$, i.e., $e^{tA}\mathrm{Pos}(K)\subseteq\mathrm{Pos}(K)$ holds
Philipp Di Dio, Konrad Schmüdgen
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Position Preserving Multi-Output Prediction [PDF]
, 2013 There is a growing demand for multiple output prediction methods capable of both minimizing residual errors and capturing the joint distribution of the response variables in a realistic and consistent fashion. Unfortunately, current methods are designed to optimize one of the two criteria, but not both.
Zubin Abraham +5 more
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, 2017 This paper is being completely rewritten, with the focus now on kernels on arbitrary domains, and the ensuing analysis. This includes Polya frequency functions/sequences, Hankel and other Toeplitz kernels, and the study of their ...
Belton, Alexander +3 more
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Schur polynomials and matrix positivity preservers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2020 A classical result by Schoenberg (1942) identifies all real-valued functions that preserve positive semidefi- niteness (psd) when applied entrywise to matrices of arbitrary dimension. Schoenberg's work has continued to attract significant interest, including renewed recent attention due to applications in high-dimensional statistics. However, despite a
Belton A, Guillot D, Khare A, Putinar M
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Fitting Constrained Continuous Spline Curves. [PDF]
, 2003 Fitting a curve through a set of planar data which represents a positive quantity requires that the curve stays above the horizontal axis, The more general problem of designing parametric and non-parametric curves which do not cross the given constraint
Ong, B. H., Kong, V.P.
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