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Varying-Coefficient Additive Models with Density Responses and Functional Auto-Regressive Error Process. [PDF]
Han Z, Li T, You J, Balakrishnan N.
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Performer-KAN-Based Failure Prediction for IGBT with BO-CEEMDAN. [PDF]
Xiao Y, Wang F.
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Characterization and estimation of heterogeneous spatial autocorrelation in spatial autoregressive models. [PDF]
Zhao J, Pu Y.
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Parameter uniform finite difference formulation with oscillation free for solving singularly perturbed delay parabolic differential equation via exponential spline. [PDF]
Hassen ZI, Duressa GF.
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Multidimensional Spline Approximation
SIAM Journal on Numerical Analysis, 1980Summary: We give direct and inverse estimates for multivariate spline approximation. The direct estimates rest on new results for local polynomial approximation which generalize the work of Brudnyi and Bramble-Hilbert. The inverse estimates are multivariate extensions of one variable ideas.
Dahmen, W., De Vore, R., Scherer, K.
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Nonlinear Nonnested Spline Approximation
Constructive Approximation, 2016Linear and in particular non-linear spline approximation is a most useful tool in the approximation of for instance two-dimensional functions. Usually, piecewise polynomial splines with more and more refined knot-sequences are considered as elements of nested spaces spanned by splines. Generalising from this point of view, it is interesting to consider
Lind, Martin, Petrushev, Pencho
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Biorthogonal Approximation by Splines
Journal of Mathematical Sciences, 2014For bi-infinite grids of points in one dimension on intervals, bi-orthogonal approximations by splines are considered. Explicit expressions for the representation of the splines are derived and specified in detail in the special case of quadratic splines. Error estimated are provided as well in a variety of approaches.
Dem'yanovich, Yu. K., Lebedeva, A. V.
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On Monotone Spline Approximation
SIAM Journal on Mathematical Analysis, 1994For a monotone function \(f\) on the interval \([0,1]\) define \(E_{n,m} (f)=\inf \| f-s\|\) with the uniform norm \(\|\cdot \|\). The infimum is taken over all monotone splines \(s\) of order \(m+1\) on \(n+1\) equidistant knots. It is known that for \(f\in C^ j\) the estimate \(E_{n,m}(f)\leq C(m) n^{-j} \omega(f^{(j)}, n^{-1})\) holds for \(0\leq j ...
Yu, X. M., Zhou, S. P.
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SPLINE APPROXIMATIONS ON MANIFOLDS
International Journal of Wavelets, Multiresolution and Information Processing, 2006A method of construction of the local approximations in the case of functions defined on n-dimensional (n ≥ 1) smooth manifold with boundary is proposed. In particular, spline and finite-element methods on manifold are discussed. Nondegenerate simplicial subdivision of the manifold is introduced and a simple method for evaluations of approach is ...
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Convex Approximation by Splines
SIAM Journal on Mathematical Analysis, 1981Jackson type estimates are obtained for the approximation of convex functions by convex splines with equally spaced knots. The results are of the same order as the Jackson type estimates for unconstrained approximation by splines with equally spaced knots.
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