DOI: 10.1016/s0893-6080(97)00010-5. Approximations of Functions by a Multilayer Perceptron: a New Approach

Approximations of Functions by a Multilayer Perceptron: a New Approach

10.1016/s0893-6080(97)00010-5

Crossref journal-article

Elsevier BV

Neural Networks (78)

Bibliography

Attali, J.-G., & PagÃ¨s, G. (1997). Approximations of Functions by a Multilayer Perceptron: a New Approach. Neural Networks, 10(6), 1069â1081.

Authors 2

Jean-Gabriel Attali (first)
Gilles Pagès (additional)

References 14 Referenced 115

10.1109/18.256500 / IEEE Transactions on Information Theory / Universal approximation bounds for superposition of a sigmoidal function by Barron (1993)
10.1007/BF01171759 / Manuscripta Math / Optimal non-linear approximation by DeVore (1994)
Ellacott, S.W. (1994). Aspects of the numerical analysis of neural networks. In A. Iserles (Ed.), Acta Numerica (pp. 145–202). Cambridge University Press, Cambridge. (10.1017/S0962492900002439)
10.1016/S0893-6080(09)80018-X / Neural Networks / Some new results on neural network approximation by Hornik (1993)
10.1016/0893-6080(89)90020-8 / Neural Networks / Multilayer feedforward networks are universal approximators by Hornik (1989)
10.1016/0893-6080(90)90005-6 / Neural Networks / Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks by Hornik (1990)
10.1162/neco.1994.6.6.1262 / Neural Computation / Degree of approximation results for feedforward networks approximating unknown mappings and their derivatives by Hornik (1994)
10.1016/S0893-6080(05)80131-5 / Neural Networks / Multilayer feedforward networks with non-polynomial activation function can approximate any function by Leshno (1993)
Light, W. (1992). Ridge functions, sigmoidal functions and neural networks. In E.W. Cheney, C.K. Chui, & L.L. Schumaker (Eds.), Approximation theory (pp. VII.i-44). Academic Press, Boston.
Lorentz, G.G. (1966). Approximation of functions. New York: Chelsea.
Lorentz, G.G. (1986). Bernstein polynomials. New York: Chelsea.
{'key': '10.1016/S0893-6080(97)00010-5_BIB12', 'first-page': '190', 'article-title': 'Neural networks for localised approximation of smooth and analytic functions', 'volume': '3', 'author': 'Mhaskar', 'year': '1993', 'journal-title': 'Neural Networks'} / Neural Networks / Neural networks for localised approximation of smooth and analytic functions by Mhaskar (1993)
Schwartz, L. (1973). Théorie des distributions. Paris: Hermann.
Timan, A.F. (1963). Theory of approximation of functions of a real variable. New York: Macmillan.

Dates

Type	When
Created	23 years ago (July 25, 2002, 6:54 p.m.)
Deposited	6 years, 4 months ago (April 18, 2019, 1:26 p.m.)
Indexed	2 months, 1 week ago (June 12, 2025, 5:26 a.m.)
Issued	28 years ago (Aug. 1, 1997)
Published	28 years ago (Aug. 1, 1997)
Published Print	28 years ago (Aug. 1, 1997)

Funders 0

None

BibTeX

@article{Attali_1997, title={Approximations of Functions by a Multilayer Perceptron: a New Approach}, volume={10}, ISSN={0893-6080}, url={http://dx.doi.org/10.1016/s0893-6080(97)00010-5}, DOI={10.1016/s0893-6080(97)00010-5}, number={6}, journal={Neural Networks}, publisher={Elsevier BV}, author={Attali, Jean-Gabriel and Pagès, Gilles}, year={1997}, month=aug, pages={1069–1081} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        6,
        12
      ]
    ],
    "date-time": "2025-06-12T09:26:20Z",
    "timestamp": 1749720380647
  },
  "reference-count": 14,
  "publisher": "Elsevier BV",
  "issue": "6",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1997,
            8,
            1
          ]
        ],
        "date-time": "1997-08-01T00:00:00Z",
        "timestamp": 870393600000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://www.elsevier.com/tdm/userlicense/1.0/"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1997,
        8
      ]
    ]
  },
  "DOI": "10.1016/s0893-6080(97)00010-5",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        25
      ]
    ],
    "date-time": "2002-07-25T22:54:47Z",
    "timestamp": 1027637687000
  },
  "page": "1069-1081",
  "source": "Crossref",
  "is-referenced-by-count": 115,
  "title": "Approximations of Functions by a Multilayer Perceptron: a New Approach",
  "prefix": "10.1016",
  "volume": "10",
  "author": [
    {
      "given": "Jean-Gabriel",
      "family": "Attali",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "Gilles",
      "family": "Pag\u00e8s",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "78",
  "reference": [
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB1",
      "doi-asserted-by": "crossref",
      "first-page": "930",
      "DOI": "10.1109/18.256500",
      "article-title": "Universal approximation bounds for superposition of a sigmoidal function",
      "volume": "39",
      "author": "Barron",
      "year": "1993",
      "journal-title": "IEEE Transactions on Information Theory"
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB2",
      "doi-asserted-by": "crossref",
      "first-page": "469",
      "DOI": "10.1007/BF01171759",
      "article-title": "Optimal non-linear approximation",
      "volume": "63",
      "author": "DeVore",
      "year": "1994",
      "journal-title": "Manuscripta Math"
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB3",
      "doi-asserted-by": "crossref",
      "unstructured": "Ellacott, S.W. (1994). Aspects of the numerical analysis of neural networks. In A. Iserles (Ed.), Acta Numerica (pp. 145\u2013202). Cambridge University Press, Cambridge.",
      "DOI": "10.1017/S0962492900002439"
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB4",
      "doi-asserted-by": "crossref",
      "first-page": "1069",
      "DOI": "10.1016/S0893-6080(09)80018-X",
      "article-title": "Some new results on neural network approximation",
      "volume": "6",
      "author": "Hornik",
      "year": "1993",
      "journal-title": "Neural Networks"
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB5",
      "doi-asserted-by": "crossref",
      "first-page": "359",
      "DOI": "10.1016/0893-6080(89)90020-8",
      "article-title": "Multilayer feedforward networks are universal approximators",
      "volume": "2",
      "author": "Hornik",
      "year": "1989",
      "journal-title": "Neural Networks"
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB6",
      "doi-asserted-by": "crossref",
      "first-page": "351",
      "DOI": "10.1016/0893-6080(90)90005-6",
      "article-title": "Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks",
      "volume": "3",
      "author": "Hornik",
      "year": "1990",
      "journal-title": "Neural Networks"
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB7",
      "doi-asserted-by": "crossref",
      "first-page": "1262",
      "DOI": "10.1162/neco.1994.6.6.1262",
      "article-title": "Degree of approximation results for feedforward networks approximating unknown mappings and their derivatives",
      "volume": "6",
      "author": "Hornik",
      "year": "1994",
      "journal-title": "Neural Computation"
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB8",
      "doi-asserted-by": "crossref",
      "first-page": "861",
      "DOI": "10.1016/S0893-6080(05)80131-5",
      "article-title": "Multilayer feedforward networks with non-polynomial activation function can approximate any function",
      "volume": "6",
      "author": "Leshno",
      "year": "1993",
      "journal-title": "Neural Networks"
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB9",
      "unstructured": "Light, W. (1992). Ridge functions, sigmoidal functions and neural networks. In E.W. Cheney, C.K. Chui, & L.L. Schumaker (Eds.), Approximation theory (pp. VII.i-44). Academic Press, Boston."
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB10",
      "unstructured": "Lorentz, G.G. (1966). Approximation of functions. New York: Chelsea."
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB11",
      "unstructured": "Lorentz, G.G. (1986). Bernstein polynomials. New York: Chelsea."
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB12",
      "first-page": "190",
      "article-title": "Neural networks for localised approximation of smooth and analytic functions",
      "volume": "3",
      "author": "Mhaskar",
      "year": "1993",
      "journal-title": "Neural Networks"
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB13",
      "unstructured": "Schwartz, L. (1973). Th\u00e9orie des distributions. Paris: Hermann."
    },
    {
      "key": "10.1016/S0893-6080(97)00010-5_BIB14",
      "unstructured": "Timan, A.F. (1963). Theory of approximation of functions of a real variable. New York: Macmillan."
    }
  ],
  "container-title": "Neural Networks",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0893608097000105?httpAccept=text/xml",
      "content-type": "text/xml",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0893608097000105?httpAccept=text/plain",
      "content-type": "text/plain",
      "content-version": "vor",
      "intended-application": "text-mining"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2019,
        4,
        18
      ]
    ],
    "date-time": "2019-04-18T17:26:45Z",
    "timestamp": 1555608405000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://linkinghub.elsevier.com/retrieve/pii/S0893608097000105"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1997,
        8
      ]
    ]
  },
  "references-count": 14,
  "journal-issue": {
    "issue": "6",
    "published-print": {
      "date-parts": [
        [
          1997,
          8
        ]
      ]
    }
  },
  "alternative-id": [
    "S0893608097000105"
  ],
  "URL": "http://dx.doi.org/10.1016/S0893-6080(97)00010-5",
  "relation": {},
  "ISSN": [
    "0893-6080"
  ],
  "subject": [],
  "container-title-short": "Neural Networks",
  "published": {
    "date-parts": [
      [
        1997,
        8
      ]
    ]
  }
}