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Body-Ordered Approximations of Atomic Properties [PDF]
Archive for Rational Mechanics and Analysis, 2022 AbstractWe show that the local density of states (LDOS) of a wide class of tight-binding models has a weak body-order expansion. Specifically, we prove that the resulting body-order expansion for analytic observables such as the electron density or the energy has an exponential rate of convergence both at finite Fermi-temperature as well as for ...
Jack Thomas +2 more
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Consistent Approximation of Fractional Order Operators [PDF]
Journal of Dynamic Systems, Measurement, and Control, 2021 Abstract Fractional order controllers become increasingly popular due to their versatility and superiority in various performances. However, the bottleneck in deploying these tools in practice is related to their analog or numerical implementation.
Wei, Yiheng +3 more
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Higher-order properties of approximate estimators [PDF]
Journal of Econometrics, 2013 Many modern estimation methods in econometrics approximate an objective function, for instance, through simulation or discretization. These approximations typically affect both bias and variance of the resulting estimator. We first provide a higher-order expansion of such "approximate" estimators that takes into account the errors due to the use of ...
Kristensen, Dennis, Salanie, Bernard
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On the Approximability of Digraph Ordering [PDF]
Algorithmica, 2015 Given an n-vertex digraph D = (V, A) the Max-k-Ordering problem is to compute a labeling $\ell : V \to [k]$ maximizing the number of forward edges, i.e. edges (u,v) such that $\ell$(u) < $\ell$(v). For different values of k, this reduces to Maximum Acyclic Subgraph (k=n), and Max-Dicut (k=2).
Kenkre, Sreyash +3 more
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Controlled approximation and a characterization of the local approximation order [PDF]
Proceedings of the American Mathematical Society, 1985 The local approximation order from a scale ( S h ) ({S_h}) of approximating functions on R m {{\mathbf {R}}^m} is characterized in terms of the linear span (and its ...
de Boor, C., Jia, R.-Q.
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Approximate Derivations of Order n [PDF]
Acta Mathematica Hungarica, 2014 The aim of this paper is to prove characterization theorems for higher order derivations. Among others we prove that the system defining higher order derivations is stable. Further characterization theorems in the spirit of N.~G.~de Bruijn will also be presented.
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Higher order approximation of isochrons [PDF]
Nonlinearity, 2010 Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction of a single oscillator, one needs to obtain the gradient of the phase function, which essentially provides a ...
Takeshita, Daisuke, Feres, Renato
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The approximation order of polysplines [PDF]
Proceedings of the American Mathematical Society, 2003 We show that the scaling spaces defined by the polysplines of order p p provide approximation order 2 p . 2p. For that purpose we refine the results on one-dimensional approximation order by L L -splines obtained by de Boor, DeVore, and Ron (1994).
Kounchev, Ognyan, Render, Hermann
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Coordinate Order of Approximation by Functional-Based Approximation Operators
Journal of Approximation Theory, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Burchard, H.G., Lei, J.J.
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The Approximation Order of Box Spline Spaces [PDF]
Proceedings of the American Mathematical Society, 1993 Let M M be a box spline associated with an arbitrary set of directions and suppose that S ( M ) S(M) is the space spanned by the integer translates of M M . In this note, the subspace of all polynomials in S ( M ) S(M) is ...
Ron, A., Sivakumar, N.
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