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

Συγγραφείς: David Schneider, Benjamin Uekermann

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

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

Συγγραφείς: Johannes Hertrich

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Baptista, Ricardo, Hosseini, Bamdad, Kovachki, Nikola B., Marzouk, Youssef, Sagiv, Amir

Πηγή: Mathematics of Computation. 94:1863-1909

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Ziyuan Liu, Haifeng Wang, Hong Zhang, Kaijun Bao, Xu Qian, Songhe Song

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Hassan Khosravian-Arab, Mehdi Dehghan

Πηγή: Computational and Applied Mathematics. 44

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Francesco Romor, Giovanni Stabile, Gianluigi Rozza

Πηγή: Journal of Computational Physics. 524:113729

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: http://arxiv.org/abs/2308.03396

Deep Neural Networks: A Formulation Via Non-Archimedean Analysis

Συγγραφείς: Zuniga-Galindo, Wilson A.

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

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

Περιγραφή αρχείου: application/pdf

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

Διαθεσιμότητα: 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

Συγγραφείς: Randa Chalekh, El Amir Djeffal

Πηγή: Asian-European Journal of Mathematics. 16

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

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

Συγγραφείς: Mlinarić, Petar, Benner, Peter, Gugercin, Serkan

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Heinrich, Stefan

Πηγή: Journal of Complexity. 81:101821

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Paul G. Constantine, Troy Butler, Tim Wildey

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

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

Συγγραφείς: Tom Lyche, Karl Scherer

Πηγή: Multivariate Approximation and Splines ISBN: 9783034898089

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Yu. Brudnyĭ

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Peter Smereka

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

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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 \(\mathbb R^d\)

Συγγραφείς: Piotr Gajda

Πηγή: Numerical Algorithms. 40:401-414

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: BINUCCI, Carla, DIDIMO, WALTER, LIOTTA, Giuseppe, Nonato M.

Πηγή: Computational Geometry. 32:71-114

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Yu Chen, Jianguo Huang

Πηγή: Inverse Problems. 21:1667-1684

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

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: 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

Συγγραφείς: Tupelly, Kavitha, Kreinovich, Vladik, Villaverde, Karen

Πηγή: Reliable Computing. 11:291-312

Θεματικοί όροι: 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

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: 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

Locally tensor product functions

Συγγραφείς: Christophe Rabut

Πηγή: Numerical Algorithms. 39:329-348

Θεματικοί όροι: tensor product function, Spline approximation, subdomains, Algorithms for approximation of functions, B-splines, Multidimensional problems, 0101 mathematics, 01 natural sciences, local refinement

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2170146
https://doi.org/10.1007/s11075-004-3646-5
https://link.springer.com/article/10.1007/s11075-004-3646-5
https://doi.org/10.1007/s11075-004-3646-5
https://ui.adsabs.harvard.edu/abs/2005NuAlg..39..329R/abstract
https://dblp.uni-trier.de/db/journals/na/na39.html#Rabut05

Generalized Approximate Weak Greedy Algorithms: Generalized approximate weak greedy algorithms

Συγγραφείς: Vladimir V. Galatenko, E. D. Livshits

Πηγή: Mathematical Notes. 78:170-184

Θεματικοί όροι: matching pursuit, convergence, pure greedy algorithms, Algorithms for approximation of functions, orthonormal system in Hilbert space, Approximation by arbitrary nonlinear expressions, widths and entropy, 0101 mathematics, General theory of numerical analysis in abstract spaces, 01 natural sciences, nonlinear approximation, dictionary

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/2239736
https://doi.org/10.1007/s11006-005-0113-0
https://link.springer.com/article/10.1007/s11006-005-0113-0