Learning PDEs from Data on Closed Surfaces with Sparse Optimization: Learning PDEs from data on closed surfaces with sparse optimization

Authors: Sun, Zhengjie, Ling, Leevan, Zhang, Ran

Source: Communications in Computational Physics. 37:289-314

Subject Terms: meshless methods, data-driven modeling, Numerical radial basis function approximation, FOS: Mathematics, FOS: Physical sciences, surface PDE, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Mathematical Physics (math-ph), sparse optimization, Interpolation in approximation theory, Mathematical Physics

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Access URL: http://arxiv.org/abs/2405.06199
https://zbmath.org/8033878
https://doi.org/10.4208/cicp.oa-2024-0112

A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces: A meshfree RBF-FD constant along normal method for solving PDEs on surfaces

Authors: Víctor Bayona, Argyrios Petras, Cécile Piret, Steven J. Ruuth

Contributors: Comunidad de Madrid

Source: e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid
Universidad Carlos III de Madrid (UC3M)

Subject Terms: Finite difference methods for boundary value problems involving PDEs, Matemáticas, Closest point method, Meshfree, Numerical Analysis (math.NA), meshfree, Numerical differentiation, Approximation by polynomials, Spline approximation, High-order methods, Numerical interpolation, Finite difference methods for initial value and initial-boundary value problems involving PDEs, high-order methods, PDEs on surfaces, FOS: Mathematics, RBF-FD, Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Interpolation in approximation theory, Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs, closest point method

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Access URL: http://arxiv.org/abs/2412.14761
https://hdl.handle.net/10016/46963

The approximation capabilities of Durrmeyer-type neural network operators

Authors: Lucian Coroianu, Danilo Costarelli, Mariarosaria Natale, Alexandra Pantiş

Source: Journal of Applied Mathematics and Computing. 70:4581-4599

Subject Terms: Lebesgue spaces, order of approximation, modulus of continuity, quantitative estimates, 0202 electrical engineering, electronic engineering, information engineering, Rate of convergence, degree of approximation, 02 engineering and technology, Durrmeyer-type neural network operators, 0101 mathematics, 01 natural sciences, Interpolation in approximation theory

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Access URL: https://zbmath.org/8035074
https://doi.org/10.1007/s12190-024-02146-9

Zipper rational fractal interpolation functions

Authors: R. Pasupathi, null Vijay, A. K. B. Chand, N. S. Upadhye

Source: The Journal of Analysis. 32:3197-3226

Subject Terms: Approximation by rational functions, Fractals, convexity, positivity, Numerical interpolation, rational cubic spline, zipper, fractal interpolation function, monotonicity, Interpolation in approximation theory, Real rational functions, Numerical computation using splines

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Access URL: https://zbmath.org/7965080
https://doi.org/10.1007/s41478-024-00796-3

Yu. N. Subbotin’s Method in the Problem of Extremal Interpolation in the Mean in the Space $$L_p(\mathbb R)$$ with Overlapping Averaging Intervals: Yu. N. Subbotin's method in the problem of extremal interpolation in the mean in the space \(L_p(\mathbb{R})\) with overlapping averaging intervals

Authors: Shevaldin, V. T.

Source: Mathematical Notes. 115:1017-1029

Subject Terms: formally self-adjoint differential operator, minimal norm, extremal interpolation, uniform mesh, spline, Interpolation in approximation theory

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Product kernels are efficient and flexible tools for high-dimensional scattered data interpolation

Authors: Kristof Albrecht, Juliane Entzian, Armin Iske

Source: Advances in Computational Mathematics. 51

Subject Terms: greedy algorithms, product kernels, kernel-based approximation, FOS: Mathematics, Rate of convergence, degree of approximation, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Interpolation in approximation theory, Approximation by other special function classes

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Access URL: http://arxiv.org/abs/2312.09949
https://zbmath.org/8023797
https://doi.org/10.1007/s10444-025-10226-y

Fast finite integration method with variational limit for multi-dimensional partial differential equations

Authors: Lei, Min, Liu, Li, Wen, P. H.

Source: Engineering Analysis with Boundary Elements. 155:440-451

Subject Terms: variational limit, trapezoidal rule, Spectral, collocation and related methods for boundary value problems involving PDEs, finite integration method, Simpson rule, multi-dimensional PDEs, Interpolation in approximation theory

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Access URL: https://zbmath.org/7849411
https://doi.org/10.1016/j.enganabound.2023.06.008

On the convergence of generalized kernel-based interpolation by greedy data selection algorithms

Authors: Kristof Albrecht, Armin Iske

Source: BIT Numerical Mathematics. 65

Subject Terms: greedy data selection algorithms, generalized kernel-based interpolation, FOS: Mathematics, Rate of convergence, degree of approximation, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), multivariate scattered data approximation, 0101 mathematics, 01 natural sciences, Interpolation in approximation theory, Approximation by other special function classes

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Access URL: http://arxiv.org/abs/2407.03840

The Fekete problem in segmental polynomial interpolation

Authors: Ludovico Bruni Bruno, Wolfgang Erb

Source: BIT Numerical Mathematics. 65

Subject Terms: Numerical interpolation, polynomial approximation of differential forms, FOS: Mathematics, segmental polynomial interpolation, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), optimal design of segments, Interpolation in approximation theory, Fekete problem, 41A05, 41A25, A1A30, 65D05

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Access URL: http://arxiv.org/abs/2403.09378
https://zbmath.org/7964459
https://doi.org/10.1007/s10543-024-01047-4

Local Extremal Interpolation on the Semiaxis with the Least Value of the Norm for a Linear Differential Operator: Local extremal interpolation on the semiaxis with the least value of the norm for a linear differential operator

Authors: Shevaldin, V. T.

Source: Mathematical Notes. 113:446-452

Subject Terms: Spline approximation, generalized finite difference, uniform grid, differential operator, semiaxis, Interpolation in approximation theory, local interpolation

File Description: application/xml

Access URL: https://zbmath.org/7676235
https://doi.org/10.1134/s0001434623030148

On the monotonicity of left and right Riemann sums

Authors: Bouthat, Ludovick^{Aff1, IDs43670024000888_cor1}

Source: Sampling Theory, Signal Processing, and Data Analysis. 22(1)

On the mean convergence of interpolatory processes

Authors: Vertesi, P.

Source: Publicationes Mathematicae Debrecen. 23:229-234

Subject Terms: Approximation by polynomials, 0101 mathematics, 01 natural sciences, Interpolation in approximation theory

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Access URL: https://zbmath.org/3563642

Convergence theorems of quasi-Hermite--Fejér interpolation: Convergence theorems of quasi-Hermite-Fejer interpolation

Authors: Santa, J.

Source: Publicationes Mathematicae Debrecen. 22:23-29

Subject Terms: 0101 mathematics, 01 natural sciences, Interpolation in approximation theory

File Description: application/xml

Access URL: https://zbmath.org/3514367

Convergence of Hermite--Fejér interpolation polynomial on the extended nodes: Convergence of Hermite-Fejer interpolation polynomial on the extended nodes

Authors: Kumar, V.

Source: Publicationes Mathematicae Debrecen. 24:31-37

Subject Terms: 0101 mathematics, 01 natural sciences, Interpolation in approximation theory

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Access URL: https://zbmath.org/3595684

Some extended Hermite--Fejér interpolation processes and their convergence: Some extended Hermite-Fejer interpolation processes and their convergence

Authors: Kumar, V.

Source: Publicationes Mathematicae Debrecen. 25:285-290

Subject Terms: Approximation by polynomials, Interpolatory Polynomials, 0101 mathematics, 01 natural sciences, Interpolation in approximation theory, Hermite-Fejer Interpolation Processes

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Access URL: https://zbmath.org/3611866

Estimate of the rate of mean convergence of Hermite interpolating processes

Authors: Szabó, S.

Source: Publicationes Mathematicae Debrecen. 39:339-345

Subject Terms: Hermite interpolating process, 0101 mathematics, 01 natural sciences, Interpolation in approximation theory

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Access URL: https://zbmath.org/61530

On the Lebesgue function on infinite interval. I

Authors: Eneduanya, S. A. N.

Source: Publicationes Mathematicae Debrecen. 31:235-241

Subject Terms: orthonormal polynomial, orthonormal Hermite polynomials, Lebesgue functions, weight function, Christoffel functions, Lagrange interpolation, 0101 mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, 01 natural sciences, Interpolation in approximation theory, Laguere polynomials

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Access URL: https://zbmath.org/3905184
https://zbmath.org/4063755

On speed of mean convergence of Lagrange and Hermite interpolation based on the roots of Laguerre polynomials

Authors: Balázs, K., Joó, I.

Source: Publicationes Mathematicae Debrecen. 38:247-253

Subject Terms: Approximation by polynomials, Lagrange interpolation, Laguerre polynomials, Hermite interpolation, 0101 mathematics, 01 natural sciences, Interpolation in approximation theory

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Access URL: https://zbmath.org/22000

Extremal functional -interpolation on an arbitrary mesh on the real axis: Extremal functional \(L_p\)-interpolation on an arbitrary mesh on the real axis

Authors: Subbotin, Yurii N., Shevaldin, Valerii T.

Source: Sbornik: Mathematics. 213:556-577

Subject Terms: Best approximation, Chebyshev systems, Spline approximation, extremal interpolation, derivative, divided difference, difference equation, spline, 0101 mathematics, 01 natural sciences, Interpolation in approximation theory, Numerical computation using splines

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$L^\infty$-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition: \( L^\infty\)-error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition

Authors: Köhne, Frederik, Philipp, Friedrich M., Schaller, Manuel, Schiela, Anton, Worthmann, Karl

Subject Terms: Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces), Linear composition operators, Numerical radial basis function approximation, Dynamical Systems (math.DS), Numerical Analysis (math.NA), Approximation methods and numerical treatment of dynamical systems, interpolation, kernel EDMD, 37M99, 41A05, 47B32, 47B33, 65D12, FOS: Mathematics, regression, uniform error bounds, Mathematics - Numerical Analysis, Mathematics - Dynamical Systems, Koopman operator, reproducing kernel Hilbert space, Interpolation in approximation theory

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Access URL: http://arxiv.org/abs/2403.18809