Keywords: Multilayer feedforward neural network; Hidden layer; Sigmoidal function; Activation function; Weight; The Kolmogorov superposition theorem; 41A30; 41A63; 65D15; 68T05; 92B20;
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Keywords: Fractional Fisher equation; Chebyshev polynomials; FDM; Convergence analysis; 41A30; 65N12; 65N22;
Keywords: 41A44; 41A30; Entire functions of exponential type; Complex-valued functions; Error of best approximation; Markov's theorem; Nagy's theorem; Convolution classes;
Keywords: 41A10; 41A25; 41A29; 41A30; Monotone approximation by piecewise polynomials; Degree of pointwise approximation; Jackson-type interpolatory estimates;
Keywords: 41A30; 41A63; 42C40; 15A03; 42B10Linear independence; Integer shifts of functions; Polynomial rings; Hilbert Nullstellensatz; Compactly supported distributions
Keywords: Ternary; Approximating; Interpolating; Subdivision scheme; Laurent polynomial; 41A05; 41A25; 41A30; 65D17; 65D10;
Keywords: 41A30; 65D10Exponential curves; Non-uniqueness; Weighted nonlinear least squares
Keywords: Binary; Approximating; Interpolating; Subdivision scheme; Curves41A05; 41A25; 41A30; 65D17; 65D10
Keywords: Quantitative asymptotic formula; Pochhammer symbol; Direct estimates; Ditzian–Totik modulus of smoothness; Rate of convergence41A25; 41A30
Keywords: Ternary; Subdivision scheme; Approximating and interpolating; Mask; Curves41A05; 41A25; 41A30; 65D17; 65D10
Keywords: 60G22; 60G52; 41A30; 41A58Approximation of processes; Linear Fractional and Multifractional Stable Motions; Wavelet series representations; Haar system
Keywords: 65D10; 65C20; 41A30; 41A58Thin plate splines; Fast evaluation; Exponential approximation
Keywords: 41A30; 65L60; 65M70; 34B40; 35L70; Generalized Hermite orthogonal approximation and interpolation; Spectral method on the whole line;
Keywords: 41A20; 41A30; 41A50; 28A80Fractal operator; Fractal rational function; Fractal Müntz rational function; Copositive fractal approximant; Best approximation
Keywords: 65D32; 65-05; 41A30; 41A63Higher dimensions; Parabolic equation; Heat potential; Separated representations; Tensor product approximation
Multiquadric RBF-FD method for the convection-dominated diffusion problems base on Shishkin nodes
Keywords: Convection-dominated diffusion; Multiquadric RBF-FD method; Hybrid scheme; Shishkin nodes; Boundary layer; 41A10; 41A30; 65N06;
Error analysis of a meshless weak form method based on radial point interpolation technique for Sivashinsky equation arising in the alloy solidification problem
Keywords: 41A30; 65M99; 65N99; Sivashinsky equation; Meshless weak form methods; Radial point interpolation technique; Error estimate; Stability; Convergence analysis; Nonlinear biharmonic equation; Alloy solidification problem;
Superconvergence of kernel-based interpolation
Keywords: 41A05; 41A30; 41A65; 65D05; 65D07; 42A82; 45C05; 46E22; 47B32; 35Sxx; RBF; Convergence; Error bounds; Boundary conditions; Pseudodifferential operators;
A note on the equioscillation theorem for best ridge function approximation
Keywords: primary; 41A30; 41A50; secondary; 46B50; 46E15; Ridge function; Chebyshev equioscillation theorem; A best approximation; Path; Weak* convergence;
Signal recovery by discrete approximation and a Prony-like method
Keywords: 41A30; 41A50; 49M25; 65F20; 90C08; 94A12; Discrete approximation; Prony's method; Linear programming; Exponential sum; Overdetermined systems; Recovery of structured functions;
Refinable functions, functionals, and iterated function systems
Keywords: Refinable functions; Iterated function Systems; Invariant measures; Lattice equations65D07; 28A25; 41A30; 26A30
Full length articleMax-product neural network and quasi-interpolation operators activated by sigmoidal functions
Keywords: 41A25; 41A05; 41A30; 47A58; Sigmoidal functions; Neural networks operators; Uniform approximation; Order of approximation; Max-product operators;
Multivariate αα-molecules
Keywords: 41A30; 41A63; 42C40Wavelets; Shearlets; Anisotropic scaling; αα-molecules; Multiscale analysis; Nonlinear approximation
Approximation rates for interpolation of Sobolev functions via Gaussians and allied functions
Keywords: 41A30; 42A10Bandlimited functions; Interpolation; Scattered data; Gaussian interpolation
Proof of Stenger's conjecture on matrix I(â1) of Sinc methods
Keywords: 15A18; 15A42; 15B05; 15B57; 41A30; 65F15; 65T40; Sinc methods; Sinc matrix; Eigenvalue localization; Toeplitz matrix; Skew symmetry; Generating function;
A quasi-interpolation scheme for periodic data based on multiquadric trigonometric B-splines
Keywords: 41A25; 41A30; 65D10; 65D15; Quasi-interpolation; Periodic data; Trigonometric divided differences; Multiquadric trigonometric B-splines; Active contours;
Convergence of a family of neural network operators of the Kantorovich type
Keywords: 41A25; 41A30; 47A58Sigmoidal functions; Multivariate neural networks operators; Uniform approximation; LpLp-approximation; Kantorovich-type operators
Fast evaluation of system matrices w.r.t. multi-tree collections of tensor product refinable basis functions
Keywords: 41A30; 65N30; 65Y20; Tensor product approximation; Adaptivity; Sparse grids; Optimal computational complexity;
FEM with Trefftz trial functions on polyhedral elements
Keywords: 65N30; 65N38; 41A25; 41A30; BEM-based FEM; Polyhedral mesh; Convergence estimates; Non-standard finite element method;
Extremal functions in de Branges and Euclidean spaces
Keywords: 41A30; 46E22; 41A05; 41A63; Extremal functions; De Branges spaces; Exponential type; Laplace transform; Homogeneous spaces; Majorants;
Tight wave packet frames for L2(R)L2(R) and H2(R)H2(R)
Keywords: 42C15; 41A30; 39B99Hardy space; Wave packet; Tight frame
Error estimate in fractional differential equations using multiquadratic radial basis functions
Keywords: 65L20; 41A30; Fractional differential equations; Caputo derivative; Multiquadratic radial basis functions; Native spaces;
On the existence of best Mitscherlich, Verhulst, and West growth curves for generalized least-squares regression
Keywords: 41A27; 41A28; 41A30; 41A63; 65D10; 65K10; 80A30; 92C45; 92D25Growth curves; Parameter identification; Singular covariance; Weighted non-linear least squares
Quasi-interpolation for linear functional data
Keywords: 65D15; 41A25; 41A30; 37B25Quasi-interpolation; Radial basis function; Linear functional data; Numerical solution of the differential equation; Lyapunov function
Pseudospectral method for quadrilaterals
Keywords: 65N35; 41A30; 35J05Legendre–Gauss-type interpolation on quadrilaterals; Pseudospectral method
Local approximation by a variant of Bernstein–Durrmeyer operators
Keywords: 41A36; 41A25; 41A30; 26A45; 26A60Approximation by positive operators; Rate of convergence; Degree of approximation; Functions of bounded variation; Total variation; Sharp bound; Asymptotic expansions
Limit problems for interpolation by analytic radial basis functions
Keywords: 41A15; 41A25; 41A30; 41A63; 65D10Radial basis functions; Moment conditions; Preconditioning; Hermite interpolation; Polynomial interpolation
Characterization of an extremal sum of ridge functions
Keywords: 41A30; 41A50; 41A63Ridge function; Path; Extremal element
A Hermite spectral method for the computation of homoclinic orbits and associated functionals
Keywords: 34B15; 34C37; 41A30; 42C15; 65L10; 65T99Spectral methods; Homoclinic orbits; Exponential convergence; Hermite functions; Metastability
Matrix decomposition MFS algorithms for elasticity and thermo-elasticity problems in axisymmetric domains
Keywords: primary 35E05; 65F05; 35J55; 65N35; secondary 35J40; 41A30; 65N38Method of fundamental solutions; Elliptic systems; Cauchy–Navier equations; Thermo-elastostatics; Circulant matrices; Fast Fourier transform; Fast algorithms
Localized sampling in the presence of noise
Keywords: primary; 41A80; 41A30; secondary; 65D25; 65G99; 94A24Localized sampling; Noise; Average sampling; Jitter error; Amplitude error
Interpolation of Lipschitz functions
Keywords: 65D05; 41A05; 41A30; 41A50; 41A63Scattered data interpolation; Lipschitz approximation; Optimal interpolation; Central algorithm; Multivariate approximation
Scattered node compact finite difference-type formulas generated from radial basis functions
Keywords: 41A21; 41A30; 41A63; 65D25; 65N06Radial basis functions; Partial differential equations; Finite difference method; Compact; Mehrstellenverfahren; Mesh-free
On the Bézier variant of generalized Kantorovich type Balazs operators
Keywords: 41A30; 41A36; Balazs operators; Rate of convergence; Bounded variation; Total variation; Bézier basis;
Local approximation by Beta operators
Keywords: 41A36; 41A25; 41A30; 26A45; 26A60; Approximation by positive operators; Rate of convergence; Degree of approximation; Functions of bounded variation; Total variation; Asymptotic expansions;
Approximation orders of shift-invariant subspaces of W2s(Rd)
Keywords: 41A25; 41A63; 41A30; 41A15; 42B99; 46E30; Approximation order; Shift-invariant spaces; Sobolev spaces; Polynomial reproduction; Strang-Fix conditions; Refinement equation; Sum rules; Superfunction;