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- 1.0524108 - ÚI 2021 RIV US eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Approximative Compactness of Linear Combinations of Characteristic Functions.
Journal of Approximation Theory. Roč. 257, September 2020 (2020), č. článku 105435. ISSN 0021-9045. E-ISSN 1096-0430
R&D Projects: GA ČR(CZ) GA18-23827S
Institutional support: RVO:67985807
Keywords : Approximative compactness * Compact sets of characteristic (indicator) functions * Symmetric difference metric * Hausdorff metric * Haar measure * Neural networks
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 1.091, year: 2020
Method of publishing: Limited access
http://dx.doi.org/10.1016/j.jat.2020.105435
Permanent Link: http://hdl.handle.net/11104/0308450 - 2.0404318 - UIVT-O 20030003 RIV US eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Best Approximation by Linear Combinations of Characteristic Functions of Half-Spaces.
Journal of Approximation Theory. Roč. 122, č. 2 (2003), s. 151-159. ISSN 0021-9045. E-ISSN 1096-0430
R&D Projects: GA ČR GA201/99/0092; GA ČR GA201/02/0428
Institutional research plan: AV0Z1030915
Keywords : best approximation * proximinal * approximatively compact * boundedly compact * heaviside perceptron networks * plane waves
Subject RIV: BA - General Mathematics
Impact factor: 0.528, year: 2003
Permanent Link: http://hdl.handle.net/11104/0124577 - 3.0403954 - UIVT-O 20000100 RIV CZ eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
An Integral Formula for Heaviside Neural Networks.
Neural Network World. Roč. 10, č. 3 (2000), s. 313-319. ISSN 1210-0552.
[Neural Network World 2000. Prague, 09.07.2000-12.07.2000]
R&D Projects: GA ČR GA201/99/0092
Institutional research plan: AV0Z1030915
Keywords : feedforward neural network * one-hidden-layer network * Heaviside function * plane wave * integral formula * numerical quadrature * Laplacian * Green's function * perceptron
Subject RIV: BA - General Mathematics
Permanent Link: http://hdl.handle.net/11104/0003431 - 4.0403756 - UIVT-O 20000030 RIV US eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Best Approximation by Heaviside Perceptron Networks.
Neural Networks. Roč. 13, č. 7 (2000), s. 695-697. ISSN 0893-6080. E-ISSN 1879-2782
R&D Projects: GA ČR GA201/96/0917; GA AV ČR IAA2030602
Institutional research plan: AV0Z1030915
Keywords : one-hidden-layer networks * heaviside perceptrons * best approximation * metric projection * continuous selection * approximatively compact
Subject RIV: BA - General Mathematics
Impact factor: 1.221, year: 2000
Permanent Link: http://hdl.handle.net/11104/0124048 - 5.0403687 - UIVT-O 20010005 RIV NL eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Continuity of Approximation by Neural Networks in Lp Spaces.
Annals of Operations Research. Roč. 101, č. 1-4 (2001), s. 143-147. ISSN 0254-5330. E-ISSN 1572-9338
R&D Projects: GA ČR GA201/99/0092
Institutional research plan: AV0Z1030915
Keywords : Chebyshev set * strictly convex space * boundedly compact * continuous selection * near best approximation
Subject RIV: BA - General Mathematics
Impact factor: 0.255, year: 2001
Permanent Link: http://hdl.handle.net/11104/0123984 - 6.0403663 - UIVT-O 20000019 RIV US eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Geometry and Topology of Continuous Best and Near Best Approximations.
Journal of Approximation Theory. Roč. 105, č. 2 (2000), s. 252-262. ISSN 0021-9045. E-ISSN 1096-0430
R&D Projects: GA ČR GA201/99/0092; GA AV ČR IAA2030602; GA ČR GA201/00/1489
Institutional research plan: AV0Z1030915
Keywords : best approximation * near best approximation * continuous selection * Chebyshev set * strictly convex space * uniformly convex space * conctraible set * tangent hypercone * modulus of convexity * Chebyshev radius
Subject RIV: BA - General Mathematics
Impact factor: 0.556, year: 2000
Permanent Link: http://hdl.handle.net/11104/0123961File Download Size Commentary Version Access 0403663.pdf 1 326.6 KB Author´s preprint open-access - 7.0403383 - UIVT-O 990036 RIV NL eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Approximation by Neural Networks is not Continuous.
Neurocomputing. Roč. 29, č. 1-3 (1999), s. 47-56. ISSN 0925-2312. E-ISSN 1872-8286
R&D Projects: GA AV ČR IAA2030602
Institutional research plan: AV0Z1030915
Subject RIV: BA - General Mathematics
Impact factor: 0.360, year: 1999
Permanent Link: http://hdl.handle.net/11104/0123694 - 8.0043643 - ÚI 2011 RIV US eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
Integral Combinations of Heavisides.
Mathematische Nachrichten. Roč. 283, č. 6 (2010), s. 854-878. ISSN 0025-584X. E-ISSN 1522-2616
R&D Projects: GA ČR GA201/05/0557; GA ČR GA201/08/1744
Institutional research plan: CEZ:AV0Z10300504
Keywords : feedforward neural network * perceptron * heaviside function * plane wave * integral formula * radon transform * Green’s function for iterated Laplacians * order of vanishing * function of controlled decay
Subject RIV: BA - General Mathematics
Impact factor: 0.653, year: 2010
Permanent Link: http://hdl.handle.net/11104/0136577 - 9.0042939 - ÚI 2008 RIV US eng J - Journal Article
Kainen, P.C. - Kůrková, Věra - Vogt, A.
A Sobolev-Type Upper Bound for Rates of Approximation by Linear Combinations of Heaviside Plane Waves.
[Horní mez Sobolevovského typu pro rychlost aproximace lineárními kombinacemi Heavisidových rovinných vln.]
Journal of Approximation Theory. Roč. 147, č. 1 (2007), s. 1-10. ISSN 0021-9045. E-ISSN 1096-0430
R&D Projects: GA MŠMT(CZ) 1M0567
Institutional research plan: CEZ:AV0Z10300504
Keywords : characteristic functions of closed half-spaces * perceptron neural networks * integral formulas * variation with respect to half-spaces * Radon transform * Gaussian function * rates of approximation
Subject RIV: IN - Informatics, Computer Science
Impact factor: 0.697, year: 2007
Permanent Link: http://hdl.handle.net/11104/0136063