Estimates of Approximation Rates by Gaussian Radial-Basis Functions View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2007

AUTHORS

Paul C. Kainen , Věra Kůrková , Marcello Sanguineti

ABSTRACT

Rates of approximation by networks with Gaussian RBFs with varying widths are investigated. For certain smooth functions, upper bounds are derived in terms of a Sobolev-equivalent norm. Coefficients involved are exponentially decreasing in the dimension. The estimates are proven using Bessel potentials as auxiliary approximating functions.

PAGES

11-18

Book

TITLE

Adaptive and Natural Computing Algorithms

ISBN

978-3-540-71590-0
978-3-540-71629-7

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-71629-7_2

DOI

http://dx.doi.org/10.1007/978-3-540-71629-7_2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1003782208


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1005", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Communications Technologies", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/10", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Technology", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Georgetown University", 
          "id": "https://www.grid.ac/institutes/grid.213910.8", 
          "name": [
            "Department of Mathematics, Georgetown University, Washington, D. C. 20057-1233, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Kainen", 
        "givenName": "Paul C.", 
        "id": "sg:person.013607306243.38", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013607306243.38"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institute of Computer Science", 
          "id": "https://www.grid.ac/institutes/grid.448092.3", 
          "name": [
            "Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vod\u00e1renskou v\u011b\u017e\u00ed 2, Prague 8, Czech Republic"
          ], 
          "type": "Organization"
        }, 
        "familyName": "K\u016frkov\u00e1", 
        "givenName": "V\u011bra", 
        "id": "sg:person.0627676237.51", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0627676237.51"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Genoa", 
          "id": "https://www.grid.ac/institutes/grid.5606.5", 
          "name": [
            "Department of Communications, Computer, and System Sciences (DIST), University of Genoa, Via Opera Pia 13, 16145 Genova, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Sanguineti", 
        "givenName": "Marcello", 
        "id": "sg:person.0677746435.25", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0677746435.25"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/978-1-4612-1996-5_16", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008720603", 
          "https://doi.org/10.1007/978-1-4612-1996-5_16"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-1996-5_16", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008720603", 
          "https://doi.org/10.1007/978-1-4612-1996-5_16"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0893-6080(97)00028-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1018224020"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1162/neco.1990.2.2.210", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025943122"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0196-8858(92)90016-p", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033587862"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1162/neco.1993.5.2.305", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044931638"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1162/neco.1991.3.2.246", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1048705139"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/18.256500", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061098999"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/18.256500", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061098999"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/18.256500", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061098999"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aos/1176348546", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064408657"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2969/jmsj/04020331", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1070931414"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1142/5314", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098871684"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2007", 
    "datePublishedReg": "2007-01-01", 
    "description": "Rates of approximation by networks with Gaussian RBFs with varying widths are investigated. For certain smooth functions, upper bounds are derived in terms of a Sobolev-equivalent norm. Coefficients involved are exponentially decreasing in the dimension. The estimates are proven using Bessel potentials as auxiliary approximating functions.", 
    "editor": [
      {
        "familyName": "Beliczynski", 
        "givenName": "Bartlomiej", 
        "type": "Person"
      }, 
      {
        "familyName": "Dzielinski", 
        "givenName": "Andrzej", 
        "type": "Person"
      }, 
      {
        "familyName": "Iwanowski", 
        "givenName": "Marcin", 
        "type": "Person"
      }, 
      {
        "familyName": "Ribeiro", 
        "givenName": "Bernardete", 
        "type": "Person"
      }
    ], 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-3-540-71629-7_2", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-3-540-71590-0", 
        "978-3-540-71629-7"
      ], 
      "name": "Adaptive and Natural Computing Algorithms", 
      "type": "Book"
    }, 
    "name": "Estimates of Approximation Rates by Gaussian Radial-Basis Functions", 
    "pagination": "11-18", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-3-540-71629-7_2"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "12048b80a23ad5eb1ec60c2a729ff8c2ccabfe3f677e03ddb4fee0038a598184"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1003782208"
        ]
      }
    ], 
    "publisher": {
      "location": "Berlin, Heidelberg", 
      "name": "Springer Berlin Heidelberg", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-3-540-71629-7_2", 
      "https://app.dimensions.ai/details/publication/pub.1003782208"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T19:06", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8684_00000245.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-3-540-71629-7_2"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-71629-7_2'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-71629-7_2'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-71629-7_2'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-3-540-71629-7_2'


 

This table displays all metadata directly associated to this object as RDF triples.

131 TRIPLES      23 PREDICATES      37 URIs      20 LITERALS      8 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-3-540-71629-7_2 schema:about anzsrc-for:10
2 anzsrc-for:1005
3 schema:author N33fd1c1143df4d33bfbbc4200ef777ee
4 schema:citation sg:pub.10.1007/978-1-4612-1996-5_16
5 https://doi.org/10.1016/0196-8858(92)90016-p
6 https://doi.org/10.1016/s0893-6080(97)00028-2
7 https://doi.org/10.1109/18.256500
8 https://doi.org/10.1142/5314
9 https://doi.org/10.1162/neco.1990.2.2.210
10 https://doi.org/10.1162/neco.1991.3.2.246
11 https://doi.org/10.1162/neco.1993.5.2.305
12 https://doi.org/10.1214/aos/1176348546
13 https://doi.org/10.2969/jmsj/04020331
14 schema:datePublished 2007
15 schema:datePublishedReg 2007-01-01
16 schema:description Rates of approximation by networks with Gaussian RBFs with varying widths are investigated. For certain smooth functions, upper bounds are derived in terms of a Sobolev-equivalent norm. Coefficients involved are exponentially decreasing in the dimension. The estimates are proven using Bessel potentials as auxiliary approximating functions.
17 schema:editor N09d9b93748204a83b14f0441074e0fc1
18 schema:genre chapter
19 schema:inLanguage en
20 schema:isAccessibleForFree false
21 schema:isPartOf Ne7ec27d0d3184092b7f768cdf7aa7985
22 schema:name Estimates of Approximation Rates by Gaussian Radial-Basis Functions
23 schema:pagination 11-18
24 schema:productId N4e4fcec1b2914130b985af3ba4c6bab0
25 N6e3a363832ea4432892bd90d24c8c33e
26 Ne03e8cdc43cc47f0bac54c1d2e9dd744
27 schema:publisher N1347b9d5ac5b4f3f883cead27a6a5d40
28 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003782208
29 https://doi.org/10.1007/978-3-540-71629-7_2
30 schema:sdDatePublished 2019-04-15T19:06
31 schema:sdLicense https://scigraph.springernature.com/explorer/license/
32 schema:sdPublisher N05498a5ca5a94e9aa935e747933b8a53
33 schema:url http://link.springer.com/10.1007/978-3-540-71629-7_2
34 sgo:license sg:explorer/license/
35 sgo:sdDataset chapters
36 rdf:type schema:Chapter
37 N05498a5ca5a94e9aa935e747933b8a53 schema:name Springer Nature - SN SciGraph project
38 rdf:type schema:Organization
39 N09d9b93748204a83b14f0441074e0fc1 rdf:first N5e8e964fb51040a2899ff3c55ef2cb01
40 rdf:rest N3f1ddbf6d714439d91d74bdd0319723b
41 N1347b9d5ac5b4f3f883cead27a6a5d40 schema:location Berlin, Heidelberg
42 schema:name Springer Berlin Heidelberg
43 rdf:type schema:Organisation
44 N29f2b7340898446ea082972d494dd0ed rdf:first Nce6a63a926664d0d8a4bdc40dde5d489
45 rdf:rest N91c5a1ae327a4929bf5727b4b3d4c2e0
46 N3191b880ba5f495a92d067fbfa8779ef schema:familyName Ribeiro
47 schema:givenName Bernardete
48 rdf:type schema:Person
49 N33fd1c1143df4d33bfbbc4200ef777ee rdf:first sg:person.013607306243.38
50 rdf:rest Nd83a81d345bc48d7b4825fcf5c0c18ca
51 N3f1ddbf6d714439d91d74bdd0319723b rdf:first Nb9d58a88703e4c9c9fb46ec9ec3a10c2
52 rdf:rest N29f2b7340898446ea082972d494dd0ed
53 N4e4fcec1b2914130b985af3ba4c6bab0 schema:name readcube_id
54 schema:value 12048b80a23ad5eb1ec60c2a729ff8c2ccabfe3f677e03ddb4fee0038a598184
55 rdf:type schema:PropertyValue
56 N5e8e964fb51040a2899ff3c55ef2cb01 schema:familyName Beliczynski
57 schema:givenName Bartlomiej
58 rdf:type schema:Person
59 N6e3a363832ea4432892bd90d24c8c33e schema:name doi
60 schema:value 10.1007/978-3-540-71629-7_2
61 rdf:type schema:PropertyValue
62 N91c5a1ae327a4929bf5727b4b3d4c2e0 rdf:first N3191b880ba5f495a92d067fbfa8779ef
63 rdf:rest rdf:nil
64 Nb9d58a88703e4c9c9fb46ec9ec3a10c2 schema:familyName Dzielinski
65 schema:givenName Andrzej
66 rdf:type schema:Person
67 Nce6a63a926664d0d8a4bdc40dde5d489 schema:familyName Iwanowski
68 schema:givenName Marcin
69 rdf:type schema:Person
70 Nd83a81d345bc48d7b4825fcf5c0c18ca rdf:first sg:person.0627676237.51
71 rdf:rest Nd8c345749dac4b498356ef8ebb6592f5
72 Nd8c345749dac4b498356ef8ebb6592f5 rdf:first sg:person.0677746435.25
73 rdf:rest rdf:nil
74 Ne03e8cdc43cc47f0bac54c1d2e9dd744 schema:name dimensions_id
75 schema:value pub.1003782208
76 rdf:type schema:PropertyValue
77 Ne7ec27d0d3184092b7f768cdf7aa7985 schema:isbn 978-3-540-71590-0
78 978-3-540-71629-7
79 schema:name Adaptive and Natural Computing Algorithms
80 rdf:type schema:Book
81 anzsrc-for:10 schema:inDefinedTermSet anzsrc-for:
82 schema:name Technology
83 rdf:type schema:DefinedTerm
84 anzsrc-for:1005 schema:inDefinedTermSet anzsrc-for:
85 schema:name Communications Technologies
86 rdf:type schema:DefinedTerm
87 sg:person.013607306243.38 schema:affiliation https://www.grid.ac/institutes/grid.213910.8
88 schema:familyName Kainen
89 schema:givenName Paul C.
90 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013607306243.38
91 rdf:type schema:Person
92 sg:person.0627676237.51 schema:affiliation https://www.grid.ac/institutes/grid.448092.3
93 schema:familyName Kůrková
94 schema:givenName Věra
95 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0627676237.51
96 rdf:type schema:Person
97 sg:person.0677746435.25 schema:affiliation https://www.grid.ac/institutes/grid.5606.5
98 schema:familyName Sanguineti
99 schema:givenName Marcello
100 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0677746435.25
101 rdf:type schema:Person
102 sg:pub.10.1007/978-1-4612-1996-5_16 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008720603
103 https://doi.org/10.1007/978-1-4612-1996-5_16
104 rdf:type schema:CreativeWork
105 https://doi.org/10.1016/0196-8858(92)90016-p schema:sameAs https://app.dimensions.ai/details/publication/pub.1033587862
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1016/s0893-6080(97)00028-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018224020
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1109/18.256500 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061098999
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1142/5314 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098871684
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1162/neco.1990.2.2.210 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025943122
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1162/neco.1991.3.2.246 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048705139
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1162/neco.1993.5.2.305 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044931638
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1214/aos/1176348546 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064408657
120 rdf:type schema:CreativeWork
121 https://doi.org/10.2969/jmsj/04020331 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070931414
122 rdf:type schema:CreativeWork
123 https://www.grid.ac/institutes/grid.213910.8 schema:alternateName Georgetown University
124 schema:name Department of Mathematics, Georgetown University, Washington, D. C. 20057-1233, USA
125 rdf:type schema:Organization
126 https://www.grid.ac/institutes/grid.448092.3 schema:alternateName Institute of Computer Science
127 schema:name Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, Prague 8, Czech Republic
128 rdf:type schema:Organization
129 https://www.grid.ac/institutes/grid.5606.5 schema:alternateName University of Genoa
130 schema:name Department of Communications, Computer, and System Sciences (DIST), University of Genoa, Via Opera Pia 13, 16145 Genova, Italy
131 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...