Search Results - "Algorithms for approximation of functions"

Effective by precision algorithms for approximation of functions from the Lipschitz class by Fourier’s series

Authors: Olena Kolomys Liliya Luts

Source: Physico-Mathematical Modelling and Informational Technologies. :111-115

Effective by precision algorithms for approximation of functions from the Gelder class by Fourier’s series

Authors: Olena Kolomys

Source: Physico-mathematical modelling and informational technologies. :159-164

Subject Terms: 0101 mathematics, 01 natural sciences

Access URL: http://www.fmmit.lviv.ua/index.php/fmmit/article/download/179/169

Efficient Partition-of-Unity Radial-Basis-Function Interpolation for Coupled Problems: Efficient partition-of-unity radial-basis-function interpolation for coupled problems

Authors: David Schneider Benjamin Uekermann

Source: SIAM Journal on Scientific Computing. 47:B558-B582

Subject Terms: partition-of-unity, Algorithms for approximation of functions, data mapping, radial-basis functions, Numerical interpolation, math software, high-performance computing, multiphysics coupling, Parallel numerical computation

File Description: application/xml

Fast Kernel Summation in High Dimensions via Slicing and Fourier Transforms: Fast kernel summation in high dimensions via slicing and Fourier transforms

Authors: Johannes Hertrich

Source: SIAM Journal on Mathematics of Data Science. 6:1109-1137

Subject Terms: FOS: Computer and information sciences, Computer Science - Machine Learning, Numerical radial basis function approximation, slicing, Numerical Analysis (math.NA), 01 natural sciences, Machine Learning (cs.LG), nonequispaced Fourier transforms, Algorithms for approximation of functions, fast kernel summation, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Numerical methods for discrete and fast Fourier transforms

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.08260
https://zbmath.org/7960206
https://doi.org/10.1137/24m1632085

An approximation theory framework for measure-transport sampling algorithms

Authors: Baptista, Ricardo Hosseini, Bamdad Kovachki, Nikola B. et al.

Source: Mathematics of Computation. 94:1863-1909

Subject Terms: Optimal transportation, transport map, generative models, Mathematics - Statistics Theory, 02 engineering and technology, Numerical Analysis (math.NA), Statistics Theory (math.ST), stability analysis, 01 natural sciences, Density estimation, Algorithms for approximation of functions, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, approximation theory

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Access URL: http://arxiv.org/abs/2302.13965

Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Nonperiodic Boundary Conditions: Render unto numerics: orthogonal polynomial neural operator for PDEs with nonperiodic boundary conditions

Authors: Ziyuan Liu Haifeng Wang Hong Zhang et al.

Source: SIAM Journal on Scientific Computing. 46:C323-C348

Subject Terms: scientific machine learning, deep learning-based PDE solver, Computational methods for problems pertaining to operator theory, Computational learning theory, spectral method, Numerical Analysis (math.NA), neural operator, 01 natural sciences, Algorithms for approximation of functions, AI4science, 0103 physical sciences, FOS: Mathematics, Mathematics - Numerical Analysis, Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs, 0101 mathematics, Artificial neural networks and deep learning

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Access URL: http://arxiv.org/abs/2206.12698
https://zbmath.org/7883828
https://doi.org/10.1137/23m1556320

A new class of gamma-type operator and its improvement: theory and numerical experiments

Authors: Hassan Khosravian-Arab Mehdi Dehghan

Source: Computational and Applied Mathematics. 44

Subject Terms: Linear operator approximation theory, Weierstrass' theorem, Approximations and expansions, Algorithms for approximation of functions, Numerical integration, positive linear operator, Voronovskaja's asymptotic formula, Korovkin theorem, Linear operator methods in interpolation, moment and extension problems, uniform convergence, second-order approximation

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Access URL: https://zbmath.org/8034210
https://doi.org/10.1007/s40314-025-03174-2

Explicable hyper-reduced order models on nonlinearly approximated solution manifolds of compressible and incompressible Navier-Stokes equations

Authors: Francesco Romor Giovanni Stabile Gianluigi Rozza

Source: Journal of Computational Physics. 524:113729

Subject Terms: scientific machine learning, Algorithms for approximation of functions, FOS: Mathematics, Computational fluid dynamics, Nonlinear model order reduction, Scientific machine learning, computational fluid dynamics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs, nonlinear model order reduction, Artificial neural networks and deep learning

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2308.03396

Deep Neural Networks: A Formulation Via Non-Archimedean Analysis

Authors: Zuniga-Galindo, Wilson A.

Source: School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Subject Terms: Artificial neural networks and deep learning, Algorithms for approximation of functions, non-Archimedean fields, p-adic analysis, Mathematics

File Description: application/pdf

Relation: https://scholarworks.utrgv.edu/mss_fac/493; https://scholarworks.utrgv.edu/context/mss_fac/article/1492/viewcontent/2402.00094v1

Availability: https://scholarworks.utrgv.edu/mss_fac/493
https://scholarworks.utrgv.edu/context/mss_fac/article/1492/viewcontent/2402.00094v1

New smoothing function for solving absolute value equations

Authors: Randa Chalekh El Amir Djeffal

Source: Asian-European Journal of Mathematics. 16

Subject Terms: convergence, smoothing function, Algorithms for approximation of functions, Numerical methods for matrix equations, 0211 other engineering and technologies, absolute value equations, 02 engineering and technology, 0101 mathematics, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), 01 natural sciences, smoothing Newton algorithm

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Interpolatory $\mathcal{H}_2$-optimality Conditions for Structured Linear Time-invariant Systems: Interpolatory \(\mathcal{H}_2\)-optimality conditions for structured linear time-invariant systems

Authors: Mlinarić, Petar Benner, Peter Gugercin, Serkan

Subject Terms: rational interpolation, linear time-invariant systems, Numerical Analysis (math.NA), Systems and Control (eess.SY), Approximation in the complex plane, Electrical Engineering and Systems Science - Systems and Control, Approximation by rational functions, Algorithms for approximation of functions, model order reduction, Optimization and Control (math.OC), Numerical interpolation, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Mathematics - Numerical Analysis, approximation, Mathematics - Optimization and Control

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Access URL: http://arxiv.org/abs/2310.10618

Randomized complexity of parametric integration and the role of adaption I. Finite dimensional case: Randomized complexity of parametric integration and the role of adaption. I: Finite dimensional case

Authors: Heinrich, Stefan

Source: Journal of Complexity. 81:101821

Subject Terms: algorithm, Analysis of algorithms and problem complexity, adaptive, Parameterized complexity, tractability and kernelization, Communication complexity, information complexity, Numerical Analysis (math.NA), General theory of numerical analysis in abstract spaces, Complexity and performance of numerical algorithms, information-based complexity, Algorithms for approximation of functions, randomized, vector-valued mean, FOS: Mathematics, nonadaptive, Mathematics - Numerical Analysis

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Access URL: http://arxiv.org/abs/2306.13471

A Posteriori Error Analysis of Parameterized Linear Systems Using Spectral Methods: A posteriori error analysis of parameterized linear systems using spectral methods

Authors: Paul G. Constantine Troy Butler Tim Wildey

Source: SIAM Journal on Matrix Analysis and Applications. 33:195-209

Subject Terms: pointwise evaluation of linear functionals, numerical examples, convergence, adjoint problem, Algorithms for approximation of functions, spectral methods, Other matrix algorithms, a posteriori error analysis, parameterized linear systems, 0101 mathematics, 01 natural sciences

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On the Sup-norm Condition Number of the Multivariate Triangular Bernstein Basis: On the \(p\)-norm condition number of the multivariate triangular Bernstein basis

Authors: Tom Lyche Karl Scherer

Source: Multivariate Approximation and Splines ISBN: 9783034898089

Subject Terms: Polynomial approximation, Applied Mathematics, Numerical computation of matrix norms, conditioning, scaling, 01 natural sciences, Multidimensional approximation, Computational Mathematics, Approximation by polynomials, multivariate Bernstein basis, Error analysis, Algorithms for approximation of functions, multidimensional approximation, Condition number, 0101 mathematics, approximation, error analysis, condition number

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Access URL: https://zbmath.org/1491261
https://doi.org/10.1016/s0377-0427(00)00383-6
https://www.sciencedirect.com/science/article/pii/S0377042700003836
https://link.springer.com/chapter/10.1007/978-3-0348-8871-4_12
https://rd.springer.com/chapter/10.1007/978-3-0348-8871-4_12
https://dialnet.unirioja.es/servlet/articulo?codigo=700122
http://ui.adsabs.harvard.edu/abs/2000JCoAM.119..259L/abstract
https://www.sciencedirect.com/science/article/pii/S0377042700003836#!

Nonlinear $N$-term approximation by refinable functions: Nonlinear \(N\)-term approximation by refinable functions

Authors: Yu. Brudnyĭ

Source: St. Petersburg Mathematical Journal. 16:143-180

Subject Terms: multivariate approximation, Algorithms for approximation of functions, Multidimensional problems, refinable function, Rate of convergence, degree of approximation, Nontrigonometric harmonic analysis involving wavelets and other special systems, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, dilation matrix, Sobolev space, Approximation by other special function classes, optimal degree of approximation, approximation algorithm, nonlinear approximation

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Access URL: https://www.ams.org/spmj/2005-16-01/S1061-0022-04-00846-5/S1061-0022-04-00846-5.pdf
https://zbmath.org/2165593
https://doi.org/10.1090/s1061-0022-04-00846-5
https://www.ams.org/spmj/2005-16-01/S1061-0022-04-00846-5/S1061-0022-04-00846-5.pdf
https://www.ams.org/journals/spmj/2005-16-01/S1061-0022-04-00846-5/home.html

The numerical approximation of a delta function with application to level set methods

Authors: Peter Smereka

Source: Journal of Computational Physics. 211:77-90

Subject Terms: Numerical solution of boundary value problems involving ordinary differential equations, Finite difference methods for boundary value problems involving PDEs, numerical examples, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Algorithms for approximation of functions, discontinuous source terms, 0103 physical sciences, elliptic equations, Linear boundary value problems for ordinary differential equations, level set methods, Poisson equation, delta function approximations, 01 natural sciences

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Access URL: https://www.sciencedirect.com/science/article/pii/S0021999105002627
https://dl.acm.org/doi/10.1016/j.jcp.2005.05.005
http://ui.adsabs.harvard.edu/abs/2006JCoPh.211...77S/abstract

Smolyak's algorithm for weighted L1-approximation of multivariate functions with bounded rth mixed derivatives over ℝd: Smolyak's algorithm for weighted \(L_1\)-approximation of multivariate functions with bounded \(r\)th mixed derivatives over \(\mathbb R^d\)

Authors: Piotr Gajda

Source: Numerical Algorithms. 40:401-414

Subject Terms: Spline approximation, Algorithms for approximation of functions, Multidimensional problems, Smolyak's algorithm, piecewise polynomial interpolation, 0101 mathematics, \(L_1\) approximation, unbounded domain, 01 natural sciences

File Description: application/xml

Access URL: https://link.springer.com/content/pdf/10.1007/s11075-005-0411-3.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=1330644
https://link.springer.com/article/10.1007%2Fs11075-005-0411-3
https://ui.adsabs.harvard.edu/abs/2005NuAlg..40..401G/abstract
https://dblp.uni-trier.de/db/journals/na/na40.html#Gajda05

Orthogonal drawings of graphs with vertex and edge labels

Authors: BINUCCI, Carla DIDIMO, WALTER LIOTTA, Giuseppe et al.

Source: Computational Geometry. 32:71-114

Subject Terms: Control and Optimization, Experimental analysis, 0102 computer and information sciences, Programming involving graphs or networks, 01 natural sciences, Planar graphs, geometric and topological aspects of graph theory, Computer Science Applications, Graph labelling (graceful graphs, bandwidth, etc.), Graph drawing, Computational Mathematics, Compaction algorithms, Labeling, Orthogonal representations, Computational Theory and Mathematics, Algorithms for approximation of functions, Graph algorithms (graph-theoretic aspects), Graph theory (including graph drawing) in computer science, Geometry and Topology

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Access URL: https://zbmath.org/2225715
https://doi.org/10.1016/j.comgeo.2005.02.001
https://dl.acm.org/doi/10.1016/j.comgeo.2005.02.001
https://www.sciencedirect.com/science/article/abs/pii/S0925772105000283
https://dblp.uni-trier.de/db/journals/comgeo/comgeo32.html#BinucciDLN05
https://www.sciencedirect.com/science/article/pii/S0925772105000283
https://core.ac.uk/display/54679954

A regularization method for the function reconstruction from approximate average fluxes

Authors: Yu Chen Jianguo Huang

Source: Inverse Problems. 21:1667-1684

Subject Terms: numerical examples, Algorithms for approximation of functions, error estimates, Tikhonov regularization, 0101 mathematics, 01 natural sciences, Numerical computation using splines, quadratic splines

File Description: application/xml

Access URL: https://zbmath.org/2218082
https://doi.org/10.1088/0266-5611/21/5/010
http://iopscience.iop.org/article/10.1088/0266-5611/21/5/010/pdf
https://iopscience.iop.org/article/10.1088/0266-5611/21/5/010/pdf
https://ui.adsabs.harvard.edu/abs/2005InvPr..21.1667H/abstract
https://iopscience.iop.org/article/10.1088/0266-5611/21/5/010

Checking If There Exists a Monotonic Function That Is Consistent with the Measurements: An Efficient Algorithm: Checking if there exist a monotonic function that is consistent with the measurements: an efficient algorithm

Authors: Tupelly, Kavitha Kreinovich, Vladik Villaverde, Karen

Source: Reliable Computing. 11:291-312

Subject Terms: monotonicity checking, 4. Education, Interval and finite arithmetic, Parallel numerical computation, 02 engineering and technology, 15. Life on land, interval uncertainty, 01 natural sciences, 7. Clean energy, Algorithms for approximation of functions, 13. Climate action, 0202 electrical engineering, electronic engineering, information engineering, Computer Engineering, 0101 mathematics, parallel computation

File Description: application/xml; application/pdf

Access URL: https://digitalcommons.utep.edu/cgi/viewcontent.cgi?article=1303&context=cs_techrep
http://www.cs.utep.edu/vladik/2004/tr04-19.pdf
https://digitalcommons.utep.edu/cs_techrep/303/
https://scholarworks.utep.edu/cs_techrep/303/
https://rd.springer.com/article/10.1007/s11155-005-6892-x
https://dblp.uni-trier.de/db/journals/rc/rc11.html#TupellyKV05
https://link.springer.com/article/10.1007/s11155-005-6892-x