Parameter Identification of Constrained Data by a New Class of Rational Fractal Function Article Swipe

PDF

S. K. Katiyar , A. K. B. Chand , Sangita Jha ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.48550/arxiv.1809.08206

This paper sets a theoretical foundation for the applications of the fractal interpolation functions (FIFs). We construct rational cubic spline FIFs (RCSFIFs) with quadratic denominator involving two shape parameters. The elements of the iterated function system (IFS) in each subinterval are identified befittingly so that the graph of the resulting $\mathcal{C}^1$-RCSFIF lies within a prescribed rectangle. These parameters include, in particular, conditions on the positivity of the $\mathcal{C}^1$-RCSFIF. The problem of visualization of constrained data is also addressed when the data is lying above a straight line, the proposed fractal curve is required to lie on the same side of the line. We illustrate our interpolation scheme with some numerical examples

Related Topics

Fractal

Rectangle

Mathematics

Mathematical Analysis

Artificial Intelligence

Evolutionary Biology

Concepts

Iterated function system Fractal Rectangle Mathematics Quadratic equation Interpolation (computer graphics) Iterated function Real line Spline (mechanical) Line (geometry) Function (biology) Applied mathematics Mathematical analysis Discrete mathematics Pure mathematics Geometry Computer science Image (mathematics) Physics Biology Artificial intelligence Thermodynamics Evolutionary biology

Metadata

Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/1809.08206
PDF: https://arxiv.org/pdf/1809.08206
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4289541750

All OpenAlex metadata

Raw OpenAlex JSON

OpenAlex ID: https://openalex.org/W4289541750

Canonical identifier for this work in OpenAlex
DOI: https://doi.org/10.48550/arxiv.1809.08206

Digital Object Identifier
Title: Parameter Identification of Constrained Data by a New Class of Rational Fractal Function

Work title
Type: preprint

OpenAlex work type
Language: en

Primary language
Publication year: 2018

Year of publication
Publication date: 2018-09-21

Full publication date if available
Authors: S. K. Katiyar, A. K. B. Chand, Sangita Jha

List of authors in order
Landing page: https://arxiv.org/abs/1809.08206

Publisher landing page
PDF URL: https://arxiv.org/pdf/1809.08206

Direct link to full text PDF
Open access: Yes

Whether a free full text is available
OA status: green

Open access status per OpenAlex
OA URL: https://arxiv.org/pdf/1809.08206

Direct OA link when available
Concepts: Iterated function system, Fractal, Rectangle, Mathematics, Quadratic equation, Interpolation (computer graphics), Iterated function, Real line, Spline (mechanical), Line (geometry), Function (biology), Applied mathematics, Mathematical analysis, Discrete mathematics, Pure mathematics, Geometry, Computer science, Image (mathematics), Physics, Biology, Artificial intelligence, Thermodynamics, Evolutionary biology

Top concepts (fields/topics) attached by OpenAlex
Cited by: 0

Total citation count in OpenAlex
Related works (count): 10

Other works algorithmically related by OpenAlex

Full payload

id	https://openalex.org/W4289541750
doi	https://doi.org/10.48550/arxiv.1809.08206
ids.doi	https://doi.org/10.48550/arxiv.1809.08206
ids.openalex	https://openalex.org/W4289541750
fwci
type	preprint
title	Parameter Identification of Constrained Data by a New Class of Rational Fractal Function
biblio.issue
biblio.volume
biblio.last_page
biblio.first_page
topics[0].id	https://openalex.org/T10588
topics[0].field.id	https://openalex.org/fields/26
topics[0].field.display_name	Mathematics
topics[0].score	0.9700999855995178
topics[0].domain.id	https://openalex.org/domains/3
topics[0].domain.display_name	Physical Sciences
topics[0].subfield.id	https://openalex.org/subfields/2610
topics[0].subfield.display_name	Mathematical Physics
topics[0].display_name	Mathematical Dynamics and Fractals
topics[1].id	https://openalex.org/T11245
topics[1].field.id	https://openalex.org/fields/22
topics[1].field.display_name	Engineering
topics[1].score	0.9337000250816345
topics[1].domain.id	https://openalex.org/domains/3
topics[1].domain.display_name	Physical Sciences
topics[1].subfield.id	https://openalex.org/subfields/2206
topics[1].subfield.display_name	Computational Mechanics
topics[1].display_name	Advanced Numerical Analysis Techniques
topics[2].id	https://openalex.org/T10688
topics[2].field.id	https://openalex.org/fields/17
topics[2].field.display_name	Computer Science
topics[2].score	0.9075000286102295
topics[2].domain.id	https://openalex.org/domains/3
topics[2].domain.display_name	Physical Sciences
topics[2].subfield.id	https://openalex.org/subfields/1707
topics[2].subfield.display_name	Computer Vision and Pattern Recognition
topics[2].display_name	Image and Signal Denoising Methods
is_xpac	False
apc_list
apc_paid
concepts[0].id	https://openalex.org/C168460219
concepts[0].level	3
concepts[0].score	0.828708291053772
concepts[0].wikidata	https://www.wikidata.org/wiki/Q1502167
concepts[0].display_name	Iterated function system
concepts[1].id	https://openalex.org/C40636538
concepts[1].level	2
concepts[1].score	0.7541563510894775
concepts[1].wikidata	https://www.wikidata.org/wiki/Q81392
concepts[1].display_name	Fractal
concepts[2].id	https://openalex.org/C2781302577
concepts[2].level	2
concepts[2].score	0.6451797485351562
concepts[2].wikidata	https://www.wikidata.org/wiki/Q209
concepts[2].display_name	Rectangle
concepts[3].id	https://openalex.org/C33923547
concepts[3].level	0
concepts[3].score	0.6145607233047485
concepts[3].wikidata	https://www.wikidata.org/wiki/Q395
concepts[3].display_name	Mathematics
concepts[4].id	https://openalex.org/C129844170
concepts[4].level	2
concepts[4].score	0.5992416739463806
concepts[4].wikidata	https://www.wikidata.org/wiki/Q41299
concepts[4].display_name	Quadratic equation
concepts[5].id	https://openalex.org/C137800194
concepts[5].level	3
concepts[5].score	0.5159583687782288
concepts[5].wikidata	https://www.wikidata.org/wiki/Q11713455
concepts[5].display_name	Interpolation (computer graphics)
concepts[6].id	https://openalex.org/C140479938
concepts[6].level	2
concepts[6].score	0.5085989236831665
concepts[6].wikidata	https://www.wikidata.org/wiki/Q5254619
concepts[6].display_name	Iterated function
concepts[7].id	https://openalex.org/C75432250
concepts[7].level	2
concepts[7].score	0.4936472177505493
concepts[7].wikidata	https://www.wikidata.org/wiki/Q29654355
concepts[7].display_name	Real line
concepts[8].id	https://openalex.org/C10390562
concepts[8].level	2
concepts[8].score	0.47642073035240173
concepts[8].wikidata	https://www.wikidata.org/wiki/Q581809
concepts[8].display_name	Spline (mechanical)
concepts[9].id	https://openalex.org/C198352243
concepts[9].level	2
concepts[9].score	0.4563567638397217
concepts[9].wikidata	https://www.wikidata.org/wiki/Q37105
concepts[9].display_name	Line (geometry)
concepts[10].id	https://openalex.org/C14036430
concepts[10].level	2
concepts[10].score	0.44849634170532227
concepts[10].wikidata	https://www.wikidata.org/wiki/Q3736076
concepts[10].display_name	Function (biology)
concepts[11].id	https://openalex.org/C28826006
concepts[11].level	1
concepts[11].score	0.3857998847961426
concepts[11].wikidata	https://www.wikidata.org/wiki/Q33521
concepts[11].display_name	Applied mathematics
concepts[12].id	https://openalex.org/C134306372
concepts[12].level	1
concepts[12].score	0.37041664123535156
concepts[12].wikidata	https://www.wikidata.org/wiki/Q7754
concepts[12].display_name	Mathematical analysis
concepts[13].id	https://openalex.org/C118615104
concepts[13].level	1
concepts[13].score	0.366807222366333
concepts[13].wikidata	https://www.wikidata.org/wiki/Q121416
concepts[13].display_name	Discrete mathematics
concepts[14].id	https://openalex.org/C202444582
concepts[14].level	1
concepts[14].score	0.323533296585083
concepts[14].wikidata	https://www.wikidata.org/wiki/Q837863
concepts[14].display_name	Pure mathematics
concepts[15].id	https://openalex.org/C2524010
concepts[15].level	1
concepts[15].score	0.2868672013282776
concepts[15].wikidata	https://www.wikidata.org/wiki/Q8087
concepts[15].display_name	Geometry
concepts[16].id	https://openalex.org/C41008148
concepts[16].level	0
concepts[16].score	0.17403504252433777
concepts[16].wikidata	https://www.wikidata.org/wiki/Q21198
concepts[16].display_name	Computer science
concepts[17].id	https://openalex.org/C115961682
concepts[17].level	2
concepts[17].score	0.09788590669631958
concepts[17].wikidata	https://www.wikidata.org/wiki/Q860623
concepts[17].display_name	Image (mathematics)
concepts[18].id	https://openalex.org/C121332964
concepts[18].level	0
concepts[18].score	0.08615180850028992
concepts[18].wikidata	https://www.wikidata.org/wiki/Q413
concepts[18].display_name	Physics
concepts[19].id	https://openalex.org/C86803240
concepts[19].level	0
concepts[19].score	0.0
concepts[19].wikidata	https://www.wikidata.org/wiki/Q420
concepts[19].display_name	Biology
concepts[20].id	https://openalex.org/C154945302
concepts[20].level	1
concepts[20].score	0.0
concepts[20].wikidata	https://www.wikidata.org/wiki/Q11660
concepts[20].display_name	Artificial intelligence
concepts[21].id	https://openalex.org/C97355855
concepts[21].level	1
concepts[21].score	0.0
concepts[21].wikidata	https://www.wikidata.org/wiki/Q11473
concepts[21].display_name	Thermodynamics
concepts[22].id	https://openalex.org/C78458016
concepts[22].level	1
concepts[22].score	0.0
concepts[22].wikidata	https://www.wikidata.org/wiki/Q840400
concepts[22].display_name	Evolutionary biology
keywords[0].id	https://openalex.org/keywords/iterated-function-system
keywords[0].score	0.828708291053772
keywords[0].display_name	Iterated function system
keywords[1].id	https://openalex.org/keywords/fractal
keywords[1].score	0.7541563510894775
keywords[1].display_name	Fractal
keywords[2].id	https://openalex.org/keywords/rectangle
keywords[2].score	0.6451797485351562
keywords[2].display_name	Rectangle
keywords[3].id	https://openalex.org/keywords/mathematics
keywords[3].score	0.6145607233047485
keywords[3].display_name	Mathematics
keywords[4].id	https://openalex.org/keywords/quadratic-equation
keywords[4].score	0.5992416739463806
keywords[4].display_name	Quadratic equation
keywords[5].id	https://openalex.org/keywords/interpolation
keywords[5].score	0.5159583687782288
keywords[5].display_name	Interpolation (computer graphics)
keywords[6].id	https://openalex.org/keywords/iterated-function
keywords[6].score	0.5085989236831665
keywords[6].display_name	Iterated function
keywords[7].id	https://openalex.org/keywords/real-line
keywords[7].score	0.4936472177505493
keywords[7].display_name	Real line
keywords[8].id	https://openalex.org/keywords/spline
keywords[8].score	0.47642073035240173
keywords[8].display_name	Spline (mechanical)
keywords[9].id	https://openalex.org/keywords/line
keywords[9].score	0.4563567638397217
keywords[9].display_name	Line (geometry)
keywords[10].id	https://openalex.org/keywords/function
keywords[10].score	0.44849634170532227
keywords[10].display_name	Function (biology)
keywords[11].id	https://openalex.org/keywords/applied-mathematics
keywords[11].score	0.3857998847961426
keywords[11].display_name	Applied mathematics
keywords[12].id	https://openalex.org/keywords/mathematical-analysis
keywords[12].score	0.37041664123535156
keywords[12].display_name	Mathematical analysis
keywords[13].id	https://openalex.org/keywords/discrete-mathematics
keywords[13].score	0.366807222366333
keywords[13].display_name	Discrete mathematics
keywords[14].id	https://openalex.org/keywords/pure-mathematics
keywords[14].score	0.323533296585083
keywords[14].display_name	Pure mathematics
keywords[15].id	https://openalex.org/keywords/geometry
keywords[15].score	0.2868672013282776
keywords[15].display_name	Geometry
keywords[16].id	https://openalex.org/keywords/computer-science
keywords[16].score	0.17403504252433777
keywords[16].display_name	Computer science
keywords[17].id	https://openalex.org/keywords/image
keywords[17].score	0.09788590669631958
keywords[17].display_name	Image (mathematics)
keywords[18].id	https://openalex.org/keywords/physics
keywords[18].score	0.08615180850028992
keywords[18].display_name	Physics
language	en
locations[0].id	pmh:oai:arXiv.org:1809.08206
locations[0].is_oa	True
locations[0].source.id	https://openalex.org/S4306400194
locations[0].source.issn
locations[0].source.type	repository
locations[0].source.is_oa	True
locations[0].source.issn_l
locations[0].source.is_core	False
locations[0].source.is_in_doaj	False
locations[0].source.display_name	arXiv (Cornell University)
locations[0].source.host_organization	https://openalex.org/I205783295
locations[0].source.host_organization_name	Cornell University
locations[0].source.host_organization_lineage	https://openalex.org/I205783295
locations[0].license
locations[0].pdf_url	https://arxiv.org/pdf/1809.08206
locations[0].version	submittedVersion
locations[0].raw_type	text
locations[0].license_id
locations[0].is_accepted	False
locations[0].is_published	False
locations[0].raw_source_name
locations[0].landing_page_url	http://arxiv.org/abs/1809.08206
locations[1].id	doi:10.48550/arxiv.1809.08206
locations[1].is_oa	True
locations[1].source.id	https://openalex.org/S4306400194
locations[1].source.issn
locations[1].source.type	repository
locations[1].source.is_oa	True
locations[1].source.issn_l
locations[1].source.is_core	False
locations[1].source.is_in_doaj	False
locations[1].source.display_name	arXiv (Cornell University)
locations[1].source.host_organization	https://openalex.org/I205783295
locations[1].source.host_organization_name	Cornell University
locations[1].source.host_organization_lineage	https://openalex.org/I205783295
locations[1].license
locations[1].pdf_url
locations[1].version
locations[1].raw_type	article
locations[1].license_id
locations[1].is_accepted	False
locations[1].is_published
locations[1].raw_source_name
locations[1].landing_page_url	https://doi.org/10.48550/arxiv.1809.08206
indexed_in	arxiv, datacite
authorships[0].author.id	https://openalex.org/A5010663214
authorships[0].author.orcid
authorships[0].author.display_name	S. K. Katiyar
authorships[0].author_position	first
authorships[0].raw_author_name	Katiyar, S. K.
authorships[0].is_corresponding	False
authorships[1].author.id	https://openalex.org/A5031211340
authorships[1].author.orcid	https://orcid.org/0000-0002-4494-0331
authorships[1].author.display_name	A. K. B. Chand
authorships[1].author_position	middle
authorships[1].raw_author_name	Chand, A. K. B.
authorships[1].is_corresponding	False
authorships[2].author.id	https://openalex.org/A5018247237
authorships[2].author.orcid
authorships[2].author.display_name	Sangita Jha
authorships[2].author_position	last
authorships[2].raw_author_name	Jha, Sangita
authorships[2].is_corresponding	False
has_content.pdf	True
has_content.grobid_xml	True
is_paratext	False
open_access.is_oa	True
open_access.oa_url	https://arxiv.org/pdf/1809.08206
open_access.oa_status	green
open_access.any_repository_has_fulltext	False
created_date	2025-10-10T00:00:00
display_name	Parameter Identification of Constrained Data by a New Class of Rational Fractal Function
has_fulltext	False
is_retracted	False
updated_date	2025-11-06T06:51:31.235846
primary_topic.id	https://openalex.org/T10588
primary_topic.field.id	https://openalex.org/fields/26
primary_topic.field.display_name	Mathematics
primary_topic.score	0.9700999855995178
primary_topic.domain.id	https://openalex.org/domains/3
primary_topic.domain.display_name	Physical Sciences
primary_topic.subfield.id	https://openalex.org/subfields/2610
primary_topic.subfield.display_name	Mathematical Physics
primary_topic.display_name	Mathematical Dynamics and Fractals
related_works	https://openalex.org/W1561687547, https://openalex.org/W2369480152, https://openalex.org/W4287710035, https://openalex.org/W2368621955, https://openalex.org/W2972725323, https://openalex.org/W3158017144, https://openalex.org/W4383425433, https://openalex.org/W2017482687, https://openalex.org/W2068677575, https://openalex.org/W2356012241
cited_by_count	0
locations_count	2
best_oa_location.id	pmh:oai:arXiv.org:1809.08206
best_oa_location.is_oa	True
best_oa_location.source.id	https://openalex.org/S4306400194
best_oa_location.source.issn
best_oa_location.source.type	repository
best_oa_location.source.is_oa	True
best_oa_location.source.issn_l
best_oa_location.source.is_core	False
best_oa_location.source.is_in_doaj	False
best_oa_location.source.display_name	arXiv (Cornell University)
best_oa_location.source.host_organization	https://openalex.org/I205783295
best_oa_location.source.host_organization_name	Cornell University
best_oa_location.source.host_organization_lineage	https://openalex.org/I205783295
best_oa_location.license
best_oa_location.pdf_url	https://arxiv.org/pdf/1809.08206
best_oa_location.version	submittedVersion
best_oa_location.raw_type	text
best_oa_location.license_id
best_oa_location.is_accepted	False
best_oa_location.is_published	False
best_oa_location.raw_source_name
best_oa_location.landing_page_url	http://arxiv.org/abs/1809.08206
primary_location.id	pmh:oai:arXiv.org:1809.08206
primary_location.is_oa	True
primary_location.source.id	https://openalex.org/S4306400194
primary_location.source.issn
primary_location.source.type	repository
primary_location.source.is_oa	True
primary_location.source.issn_l
primary_location.source.is_core	False
primary_location.source.is_in_doaj	False
primary_location.source.display_name	arXiv (Cornell University)
primary_location.source.host_organization	https://openalex.org/I205783295
primary_location.source.host_organization_name	Cornell University
primary_location.source.host_organization_lineage	https://openalex.org/I205783295
primary_location.license
primary_location.pdf_url	https://arxiv.org/pdf/1809.08206
primary_location.version	submittedVersion
primary_location.raw_type	text
primary_location.license_id
primary_location.is_accepted	False
primary_location.is_published	False
primary_location.raw_source_name
primary_location.landing_page_url	http://arxiv.org/abs/1809.08206
publication_date	2018-09-21
publication_year	2018
referenced_works_count	0
abstract_inverted_index.a	3, 53, 84
abstract_inverted_index.We	15, 102
abstract_inverted_index.in	37, 59
abstract_inverted_index.is	75, 81, 91
abstract_inverted_index.of	9, 31, 47, 65, 70, 72, 99
abstract_inverted_index.on	62, 95
abstract_inverted_index.so	43
abstract_inverted_index.to	93
abstract_inverted_index.The	29, 68
abstract_inverted_index.are	40
abstract_inverted_index.for	6
abstract_inverted_index.lie	94
abstract_inverted_index.our	104
abstract_inverted_index.the	7, 10, 32, 45, 48, 63, 66, 79, 87, 96, 100
abstract_inverted_index.two	26
abstract_inverted_index.FIFs	20
abstract_inverted_index.This	0
abstract_inverted_index.also	76
abstract_inverted_index.data	74, 80
abstract_inverted_index.each	38
abstract_inverted_index.lies	51
abstract_inverted_index.same	97
abstract_inverted_index.sets	2
abstract_inverted_index.side	98
abstract_inverted_index.some	108
abstract_inverted_index.that	44
abstract_inverted_index.when	78
abstract_inverted_index.with	22, 107
abstract_inverted_index.(IFS)	36
abstract_inverted_index.These	56
abstract_inverted_index.above	83
abstract_inverted_index.cubic	18
abstract_inverted_index.curve	90
abstract_inverted_index.graph	46
abstract_inverted_index.line,	86
abstract_inverted_index.line.	101
abstract_inverted_index.lying	82
abstract_inverted_index.paper	1
abstract_inverted_index.shape	27
abstract_inverted_index.scheme	106
abstract_inverted_index.spline	19
abstract_inverted_index.system	35
abstract_inverted_index.within	52
abstract_inverted_index.(FIFs).	14
abstract_inverted_index.fractal	11, 89
abstract_inverted_index.problem	69
abstract_inverted_index.elements	30
abstract_inverted_index.examples	110
abstract_inverted_index.function	34
abstract_inverted_index.include,	58
abstract_inverted_index.iterated	33
abstract_inverted_index.proposed	88
abstract_inverted_index.rational	17
abstract_inverted_index.required	92
abstract_inverted_index.straight	85
abstract_inverted_index.(RCSFIFs)	21
abstract_inverted_index.addressed	77
abstract_inverted_index.construct	16
abstract_inverted_index.functions	13
abstract_inverted_index.involving	25
abstract_inverted_index.numerical	109
abstract_inverted_index.quadratic	23
abstract_inverted_index.resulting	49
abstract_inverted_index.conditions	61
abstract_inverted_index.foundation	5
abstract_inverted_index.identified	41
abstract_inverted_index.illustrate	103
abstract_inverted_index.parameters	57
abstract_inverted_index.positivity	64
abstract_inverted_index.prescribed	54
abstract_inverted_index.rectangle.	55
abstract_inverted_index.befittingly	42
abstract_inverted_index.constrained	73
abstract_inverted_index.denominator	24
abstract_inverted_index.parameters.	28
abstract_inverted_index.particular,	60
abstract_inverted_index.subinterval	39
abstract_inverted_index.theoretical	4
abstract_inverted_index.applications	8
abstract_inverted_index.interpolation	12, 105
abstract_inverted_index.visualization	71
abstract_inverted_index.$\mathcal{C}^1$-RCSFIF	50
abstract_inverted_index.$\mathcal{C}^1$-RCSFIF.	67
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	3
citation_normalized_percentile