Different methods for solving STEM problems View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-09-25

AUTHORS

Ioannis K. Argyros, Á. A. Magreñán, L. Orcos, Íñígo Sarría, Juan Antonio Sicilia

ABSTRACT

We first present a local convergence analysis for some families of fourth and six order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies have used hypotheses on the fourth Fréchet-derivative of the operator involved. We use hypotheses only on the first Fréchet-derivative in one local convergence analysis. This way, the applicability of these methods is extended. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study based on Lipschitz constants. Numerical examples illustrating the theoretical results are also presented in this study. More... »

PAGES

1268-1281

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10910-018-0950-1

DOI

http://dx.doi.org/10.1007/s10910-018-0950-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107226142


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/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Mathematics Sciences, Cameron University, 73505, Lawton, OK, USA", 
          "id": "http://www.grid.ac/institutes/grid.253592.a", 
          "name": [
            "Department of Mathematics Sciences, Cameron University, 73505, Lawton, OK, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Argyros", 
        "givenName": "Ioannis K.", 
        "id": "sg:person.015707547201.06", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015707547201.06"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Departamento de Matem\u00e1ticas y Computaci\u00f3n, Universidad de La Rioja, Complejo Cient\u00edfico Tecnol\u00f3gico, Madre de Dios 53, 26006, Logro\u00f1o, La Rioja, Spain", 
          "id": "http://www.grid.ac/institutes/grid.119021.a", 
          "name": [
            "Departamento de Matem\u00e1ticas y Computaci\u00f3n, Universidad de La Rioja, Complejo Cient\u00edfico Tecnol\u00f3gico, Madre de Dios 53, 26006, Logro\u00f1o, La Rioja, Spain"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Magre\u00f1\u00e1n", 
        "givenName": "\u00c1. A.", 
        "id": "sg:person.013576636334.52", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013576636334.52"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Universidad Internacional de La Rioja, Avda de La Paz 137, 26006, Logro\u00f1o, La Rioja, Spain", 
          "id": "http://www.grid.ac/institutes/grid.13825.3d", 
          "name": [
            "Universidad Internacional de La Rioja, Avda de La Paz 137, 26006, Logro\u00f1o, La Rioja, Spain"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Orcos", 
        "givenName": "L.", 
        "id": "sg:person.016113540473.51", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016113540473.51"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Universidad Internacional de La Rioja, Avda de La Paz 137, 26006, Logro\u00f1o, La Rioja, Spain", 
          "id": "http://www.grid.ac/institutes/grid.13825.3d", 
          "name": [
            "Universidad Internacional de La Rioja, Avda de La Paz 137, 26006, Logro\u00f1o, La Rioja, Spain"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Sarr\u00eda", 
        "givenName": "\u00cd\u00f1\u00edgo", 
        "id": "sg:person.012734473367.80", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012734473367.80"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Universidad Internacional de La Rioja, Avda de La Paz 137, 26006, Logro\u00f1o, La Rioja, Spain", 
          "id": "http://www.grid.ac/institutes/grid.13825.3d", 
          "name": [
            "Universidad Internacional de La Rioja, Avda de La Paz 137, 26006, Logro\u00f1o, La Rioja, Spain"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Sicilia", 
        "givenName": "Juan Antonio", 
        "id": "sg:person.016663220241.96", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016663220241.96"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s11071-015-2179-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006090487", 
          "https://doi.org/10.1007/s11071-015-2179-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02238803", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038780485", 
          "https://doi.org/10.1007/bf02238803"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018-09-25", 
    "datePublishedReg": "2018-09-25", 
    "description": "We first present a local convergence analysis for some families of fourth and six order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies have used hypotheses on the fourth Fr\u00e9chet-derivative of the operator involved. We use hypotheses only on the first Fr\u00e9chet-derivative in one local convergence analysis. This way, the applicability of these methods is extended. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study based on Lipschitz constants. Numerical examples illustrating the theoretical results are also presented in this study.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s10910-018-0950-1", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1026076", 
        "issn": [
          "0259-9791", 
          "1572-8897"
        ], 
        "name": "Journal of Mathematical Chemistry", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "5", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "57"
      }
    ], 
    "keywords": [
      "Fr\u00e9chet-derivative", 
      "local convergence analysis", 
      "convergence analysis", 
      "first Fr\u00e9chet-derivative", 
      "computable error bounds", 
      "Banach space setting", 
      "radius of convergence", 
      "nonlinear equations", 
      "space setting", 
      "Lipschitz constants", 
      "error bounds", 
      "order method", 
      "numerical examples", 
      "unique solution", 
      "theoretical results", 
      "STEM problem", 
      "equations", 
      "convergence", 
      "operators", 
      "bounds", 
      "different methods", 
      "problem", 
      "solution", 
      "applicability", 
      "analysis", 
      "order", 
      "way", 
      "results", 
      "radius", 
      "distance", 
      "family", 
      "constants", 
      "setting", 
      "hypothesis", 
      "earlier studies", 
      "study", 
      "method", 
      "example", 
      "fourth Fr\u00e9chet-derivative"
    ], 
    "name": "Different methods for solving STEM problems", 
    "pagination": "1268-1281", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1107226142"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10910-018-0950-1"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10910-018-0950-1", 
      "https://app.dimensions.ai/details/publication/pub.1107226142"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2021-12-01T19:44", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/article/article_788.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s10910-018-0950-1"
  }
]
 

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/s10910-018-0950-1'

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/s10910-018-0950-1'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10910-018-0950-1'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10910-018-0950-1'


 

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

139 TRIPLES      22 PREDICATES      66 URIs      56 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10910-018-0950-1 schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author N788a612835244b85b8f3672b3ec539e7
4 schema:citation sg:pub.10.1007/bf02238803
5 sg:pub.10.1007/s11071-015-2179-x
6 schema:datePublished 2018-09-25
7 schema:datePublishedReg 2018-09-25
8 schema:description We first present a local convergence analysis for some families of fourth and six order methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies have used hypotheses on the fourth Fréchet-derivative of the operator involved. We use hypotheses only on the first Fréchet-derivative in one local convergence analysis. This way, the applicability of these methods is extended. Moreover, the radius of convergence and computable error bounds on the distances involved are also given in this study based on Lipschitz constants. Numerical examples illustrating the theoretical results are also presented in this study.
9 schema:genre article
10 schema:inLanguage en
11 schema:isAccessibleForFree false
12 schema:isPartOf Nd0723a717837400b803aaafc57c249d7
13 Ned7727e7f3074ee9aeffd9791fee17b4
14 sg:journal.1026076
15 schema:keywords Banach space setting
16 Fréchet-derivative
17 Lipschitz constants
18 STEM problem
19 analysis
20 applicability
21 bounds
22 computable error bounds
23 constants
24 convergence
25 convergence analysis
26 different methods
27 distance
28 earlier studies
29 equations
30 error bounds
31 example
32 family
33 first Fréchet-derivative
34 fourth Fréchet-derivative
35 hypothesis
36 local convergence analysis
37 method
38 nonlinear equations
39 numerical examples
40 operators
41 order
42 order method
43 problem
44 radius
45 radius of convergence
46 results
47 setting
48 solution
49 space setting
50 study
51 theoretical results
52 unique solution
53 way
54 schema:name Different methods for solving STEM problems
55 schema:pagination 1268-1281
56 schema:productId N3ce12291aafc4e5ab0a7fc094c3a5ee3
57 N6a7ed05c9ca041c4b881963fc9b1a8dd
58 schema:sameAs https://app.dimensions.ai/details/publication/pub.1107226142
59 https://doi.org/10.1007/s10910-018-0950-1
60 schema:sdDatePublished 2021-12-01T19:44
61 schema:sdLicense https://scigraph.springernature.com/explorer/license/
62 schema:sdPublisher N10bac35c8a3a43d98e9112cdb36304ec
63 schema:url https://doi.org/10.1007/s10910-018-0950-1
64 sgo:license sg:explorer/license/
65 sgo:sdDataset articles
66 rdf:type schema:ScholarlyArticle
67 N10bac35c8a3a43d98e9112cdb36304ec schema:name Springer Nature - SN SciGraph project
68 rdf:type schema:Organization
69 N20eb3e6c0abe41d6b2be2e120c75d9f3 rdf:first sg:person.016663220241.96
70 rdf:rest rdf:nil
71 N3ce12291aafc4e5ab0a7fc094c3a5ee3 schema:name doi
72 schema:value 10.1007/s10910-018-0950-1
73 rdf:type schema:PropertyValue
74 N62f9e639ed85459e81dfa38dd2e479bc rdf:first sg:person.016113540473.51
75 rdf:rest Na93744c994da468587097e753751e5c3
76 N6a7ed05c9ca041c4b881963fc9b1a8dd schema:name dimensions_id
77 schema:value pub.1107226142
78 rdf:type schema:PropertyValue
79 N788a612835244b85b8f3672b3ec539e7 rdf:first sg:person.015707547201.06
80 rdf:rest Na7c60e4a8fa74905b0fcbba5e65ec99d
81 Na7c60e4a8fa74905b0fcbba5e65ec99d rdf:first sg:person.013576636334.52
82 rdf:rest N62f9e639ed85459e81dfa38dd2e479bc
83 Na93744c994da468587097e753751e5c3 rdf:first sg:person.012734473367.80
84 rdf:rest N20eb3e6c0abe41d6b2be2e120c75d9f3
85 Nd0723a717837400b803aaafc57c249d7 schema:issueNumber 5
86 rdf:type schema:PublicationIssue
87 Ned7727e7f3074ee9aeffd9791fee17b4 schema:volumeNumber 57
88 rdf:type schema:PublicationVolume
89 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
90 schema:name Mathematical Sciences
91 rdf:type schema:DefinedTerm
92 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
93 schema:name Statistics
94 rdf:type schema:DefinedTerm
95 sg:journal.1026076 schema:issn 0259-9791
96 1572-8897
97 schema:name Journal of Mathematical Chemistry
98 schema:publisher Springer Nature
99 rdf:type schema:Periodical
100 sg:person.012734473367.80 schema:affiliation grid-institutes:grid.13825.3d
101 schema:familyName Sarría
102 schema:givenName Íñígo
103 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012734473367.80
104 rdf:type schema:Person
105 sg:person.013576636334.52 schema:affiliation grid-institutes:grid.119021.a
106 schema:familyName Magreñán
107 schema:givenName Á. A.
108 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013576636334.52
109 rdf:type schema:Person
110 sg:person.015707547201.06 schema:affiliation grid-institutes:grid.253592.a
111 schema:familyName Argyros
112 schema:givenName Ioannis K.
113 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015707547201.06
114 rdf:type schema:Person
115 sg:person.016113540473.51 schema:affiliation grid-institutes:grid.13825.3d
116 schema:familyName Orcos
117 schema:givenName L.
118 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016113540473.51
119 rdf:type schema:Person
120 sg:person.016663220241.96 schema:affiliation grid-institutes:grid.13825.3d
121 schema:familyName Sicilia
122 schema:givenName Juan Antonio
123 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016663220241.96
124 rdf:type schema:Person
125 sg:pub.10.1007/bf02238803 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038780485
126 https://doi.org/10.1007/bf02238803
127 rdf:type schema:CreativeWork
128 sg:pub.10.1007/s11071-015-2179-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1006090487
129 https://doi.org/10.1007/s11071-015-2179-x
130 rdf:type schema:CreativeWork
131 grid-institutes:grid.119021.a schema:alternateName Departamento de Matemáticas y Computación, Universidad de La Rioja, Complejo Científico Tecnológico, Madre de Dios 53, 26006, Logroño, La Rioja, Spain
132 schema:name Departamento de Matemáticas y Computación, Universidad de La Rioja, Complejo Científico Tecnológico, Madre de Dios 53, 26006, Logroño, La Rioja, Spain
133 rdf:type schema:Organization
134 grid-institutes:grid.13825.3d schema:alternateName Universidad Internacional de La Rioja, Avda de La Paz 137, 26006, Logroño, La Rioja, Spain
135 schema:name Universidad Internacional de La Rioja, Avda de La Paz 137, 26006, Logroño, La Rioja, Spain
136 rdf:type schema:Organization
137 grid-institutes:grid.253592.a schema:alternateName Department of Mathematics Sciences, Cameron University, 73505, Lawton, OK, USA
138 schema:name Department of Mathematics Sciences, Cameron University, 73505, Lawton, OK, USA
139 rdf:type schema:Organization
 




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


...