Unified Convergence for Multi-Point Super Halley-Type Methods with Parameters in Banach Space View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03-04

AUTHORS

Ioannis K. Argyros, Santhosh George

ABSTRACT

We present a local convergence analysis of a multi-point super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier works was based on hypotheses reaching up to the third derivative of the operator. In the present study we expand the applicability of the Super-Halley-like method by using hypotheses only on the first derivative. We also provide: A computable error on the distances involved and a uniqueness result based on Lipschitz constants. The convergence order is also provided for these methods. Numerical examples are also presented in this study. More... »

PAGES

1-13

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s13226-019-0302-2

DOI

http://dx.doi.org/10.1007/s13226-019-0302-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112520159


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 Mathematical Sciences, Cameron University, OK73505, Lawton, USA", 
          "id": "http://www.grid.ac/institutes/grid.253592.a", 
          "name": [
            "Department of Mathematical Sciences, Cameron University, OK73505, Lawton, 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": "Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, 575 025, Mangaluru, India", 
          "id": "http://www.grid.ac/institutes/grid.444525.6", 
          "name": [
            "Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, 575 025, Mangaluru, India"
          ], 
          "type": "Organization"
        }, 
        "familyName": "George", 
        "givenName": "Santhosh", 
        "id": "sg:person.016015532400.41", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016015532400.41"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s002459911012", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049334328", 
          "https://doi.org/10.1007/s002459911012"
        ], 
        "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"
      }, 
      {
        "id": "sg:pub.10.1007/s11075-011-9501-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030552333", 
          "https://doi.org/10.1007/s11075-011-9501-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11075-012-9585-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043662018", 
          "https://doi.org/10.1007/s11075-012-9585-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02241866", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008743953", 
          "https://doi.org/10.1007/bf02241866"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-03-04", 
    "datePublishedReg": "2019-03-04", 
    "description": "We present a local convergence analysis of a multi-point super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier works was based on hypotheses reaching up to the third derivative of the operator. In the present study we expand the applicability of the Super-Halley-like method by using hypotheses only on the first derivative. We also provide: A computable error on the distances involved and a uniqueness result based on Lipschitz constants. The convergence order is also provided for these methods. Numerical examples are also presented in this study.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s13226-019-0302-2", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136057", 
        "issn": [
          "0019-5588", 
          "0975-7465"
        ], 
        "name": "Indian Journal of Pure and Applied Mathematics", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "50"
      }
    ], 
    "keywords": [
      "convergence analysis", 
      "Halley-like methods", 
      "local convergence analysis", 
      "Banach space setting", 
      "convergence order", 
      "uniqueness results", 
      "Lipschitz constants", 
      "Banach spaces", 
      "space setting", 
      "type method", 
      "numerical examples", 
      "computable error", 
      "unique solution", 
      "like method", 
      "third derivative", 
      "first derivative", 
      "earlier work", 
      "equations", 
      "convergence", 
      "operators", 
      "space", 
      "solution", 
      "Halley", 
      "error", 
      "parameters", 
      "order", 
      "applicability", 
      "derivatives", 
      "constants", 
      "distance", 
      "analysis", 
      "work", 
      "results", 
      "hypothesis", 
      "setting", 
      "study", 
      "present study", 
      "method", 
      "example", 
      "Super-Halley", 
      "Unified Convergence", 
      "Multi-Point Super Halley"
    ], 
    "name": "Unified Convergence for Multi-Point Super Halley-Type Methods with Parameters in Banach Space", 
    "pagination": "1-13", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1112520159"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s13226-019-0302-2"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s13226-019-0302-2", 
      "https://app.dimensions.ai/details/publication/pub.1112520159"
    ], 
    "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_819.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s13226-019-0302-2"
  }
]
 

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/s13226-019-0302-2'

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/s13226-019-0302-2'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s13226-019-0302-2'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s13226-019-0302-2'


 

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

130 TRIPLES      22 PREDICATES      72 URIs      59 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s13226-019-0302-2 schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author Nc81242d41c2449b6bbc9843f2eb8f8c9
4 schema:citation sg:pub.10.1007/bf02238803
5 sg:pub.10.1007/bf02241866
6 sg:pub.10.1007/s002459911012
7 sg:pub.10.1007/s11075-011-9501-6
8 sg:pub.10.1007/s11075-012-9585-7
9 schema:datePublished 2019-03-04
10 schema:datePublishedReg 2019-03-04
11 schema:description We present a local convergence analysis of a multi-point super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier works was based on hypotheses reaching up to the third derivative of the operator. In the present study we expand the applicability of the Super-Halley-like method by using hypotheses only on the first derivative. We also provide: A computable error on the distances involved and a uniqueness result based on Lipschitz constants. The convergence order is also provided for these methods. Numerical examples are also presented in this study.
12 schema:genre article
13 schema:inLanguage en
14 schema:isAccessibleForFree false
15 schema:isPartOf N3b794c0d9e5649d9979bc811b67a204f
16 N90bb862cbe274e27ba3c582365b660ba
17 sg:journal.1136057
18 schema:keywords Banach space setting
19 Banach spaces
20 Halley
21 Halley-like methods
22 Lipschitz constants
23 Multi-Point Super Halley
24 Super-Halley
25 Unified Convergence
26 analysis
27 applicability
28 computable error
29 constants
30 convergence
31 convergence analysis
32 convergence order
33 derivatives
34 distance
35 earlier work
36 equations
37 error
38 example
39 first derivative
40 hypothesis
41 like method
42 local convergence analysis
43 method
44 numerical examples
45 operators
46 order
47 parameters
48 present study
49 results
50 setting
51 solution
52 space
53 space setting
54 study
55 third derivative
56 type method
57 unique solution
58 uniqueness results
59 work
60 schema:name Unified Convergence for Multi-Point Super Halley-Type Methods with Parameters in Banach Space
61 schema:pagination 1-13
62 schema:productId Ne09ec404a4284255b7a6a6d92ca96c24
63 Nf5a3d3ea10a54ab79b94e15bdb81185d
64 schema:sameAs https://app.dimensions.ai/details/publication/pub.1112520159
65 https://doi.org/10.1007/s13226-019-0302-2
66 schema:sdDatePublished 2021-12-01T19:44
67 schema:sdLicense https://scigraph.springernature.com/explorer/license/
68 schema:sdPublisher N569e6f34163d46af8d82e268bb0155e0
69 schema:url https://doi.org/10.1007/s13226-019-0302-2
70 sgo:license sg:explorer/license/
71 sgo:sdDataset articles
72 rdf:type schema:ScholarlyArticle
73 N3b794c0d9e5649d9979bc811b67a204f schema:volumeNumber 50
74 rdf:type schema:PublicationVolume
75 N569e6f34163d46af8d82e268bb0155e0 schema:name Springer Nature - SN SciGraph project
76 rdf:type schema:Organization
77 N6ac2d54df4804bb39206035ba6170685 rdf:first sg:person.016015532400.41
78 rdf:rest rdf:nil
79 N90bb862cbe274e27ba3c582365b660ba schema:issueNumber 1
80 rdf:type schema:PublicationIssue
81 Nc81242d41c2449b6bbc9843f2eb8f8c9 rdf:first sg:person.015707547201.06
82 rdf:rest N6ac2d54df4804bb39206035ba6170685
83 Ne09ec404a4284255b7a6a6d92ca96c24 schema:name dimensions_id
84 schema:value pub.1112520159
85 rdf:type schema:PropertyValue
86 Nf5a3d3ea10a54ab79b94e15bdb81185d schema:name doi
87 schema:value 10.1007/s13226-019-0302-2
88 rdf:type schema:PropertyValue
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.1136057 schema:issn 0019-5588
96 0975-7465
97 schema:name Indian Journal of Pure and Applied Mathematics
98 schema:publisher Springer Nature
99 rdf:type schema:Periodical
100 sg:person.015707547201.06 schema:affiliation grid-institutes:grid.253592.a
101 schema:familyName Argyros
102 schema:givenName Ioannis K.
103 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015707547201.06
104 rdf:type schema:Person
105 sg:person.016015532400.41 schema:affiliation grid-institutes:grid.444525.6
106 schema:familyName George
107 schema:givenName Santhosh
108 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016015532400.41
109 rdf:type schema:Person
110 sg:pub.10.1007/bf02238803 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038780485
111 https://doi.org/10.1007/bf02238803
112 rdf:type schema:CreativeWork
113 sg:pub.10.1007/bf02241866 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008743953
114 https://doi.org/10.1007/bf02241866
115 rdf:type schema:CreativeWork
116 sg:pub.10.1007/s002459911012 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049334328
117 https://doi.org/10.1007/s002459911012
118 rdf:type schema:CreativeWork
119 sg:pub.10.1007/s11075-011-9501-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030552333
120 https://doi.org/10.1007/s11075-011-9501-6
121 rdf:type schema:CreativeWork
122 sg:pub.10.1007/s11075-012-9585-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043662018
123 https://doi.org/10.1007/s11075-012-9585-7
124 rdf:type schema:CreativeWork
125 grid-institutes:grid.253592.a schema:alternateName Department of Mathematical Sciences, Cameron University, OK73505, Lawton, USA
126 schema:name Department of Mathematical Sciences, Cameron University, OK73505, Lawton, USA
127 rdf:type schema:Organization
128 grid-institutes:grid.444525.6 schema:alternateName Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, 575 025, Mangaluru, India
129 schema:name Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, 575 025, Mangaluru, India
130 rdf:type schema:Organization
 




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


...