Exponentiation of parametric Hamiltonians via unitary interpolation
Physical Review ResearchThe effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit compilation, or Monte ...
Michael Schilling +4 more
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Accuracy Assessment of LiDAR-Derived Digital Elevation Models Based on Approximation Theory
Remote Sensing, 2015 The cumulative error at a point in a LiDAR-derived DEM consists of three components: propagated LiDAR-sensor error, propagated ground error, and interpolation error.
XiaoHang Liu, Hai Hu, Peng Hu
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Approximation in Perceptual Completion
Gestalt TheoryNormally, the perception of complete visual shapes given incomplete sensory evidence can be explained by interpolation; i.e., by the smooth monotonic connection of literally represented contour stimuli.
Gerbino Walter
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Approximation of Bivariate Functions by Generalized Wendland Radial Basis Functions
MathematicsIn this work, we deal with two approximation problems in a finite-dimensional generalized Wendland space of compactly supported radial basis functions. Namely, we present an interpolation method and a smoothing variational method in this space. Next, the
Abdelouahed Kouibia +5 more
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Interpolation, Approximation and Controllability of Deep Neural Networks [PDF]
arXiv.org, 2023 We investigate the expressive power of deep residual neural networks idealized as continuous dynamical systems through control theory. Specifically, we consider two properties that arise from supervised learning, namely universal interpolation - the ...
Jingpu Cheng +3 more
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On the optimality of target-data-dependent kernel greedy interpolation in Sobolev Reproducing Kernel Hilbert Spaces [PDF]
SIAM Journal on Numerical Analysis, 2023 Kernel interpolation is a versatile tool for the approximation of functions from data, and it can be proven to have some optimality properties when used with kernels related to certain Sobolev spaces.
G. Santin, T. Wenzel, B. Haasdonk
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Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions [PDF]
Constructive approximation, 2020 We study the approximation of univariate functions by combining tensorization of functions with tensor trains (TTs)—a commonly used type of tensor networks (TNs).
Mazen Ali, A. Nouy
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Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification [PDF]
Numerische Mathematik, 2020 This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice—a setting that, as pointed out by Zeng et al. (Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, New
V. Kaarnioja +4 more
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Electronic Transactions on Numerical Analysis, 2022 . In the classical (non-fractal) setting, the natural kinship between theories of interpolation and approximation is well explored. In contrast to this, in the context of fractal interpolation, the interrelation between interpolation and approximation is
K. K. Pandey, P. Viswanathan
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Approximation and interpolation of regular maps from affine varieties to algebraic manifolds [PDF]
Mathematica Scandinavica, 2017 We consider the analogue for regular maps from affine varieties to suitable algebraic manifolds of Oka theory for holomorphic maps from Stein spaces to suitable complex manifolds.
F. Lárusson, T. Truong
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