MULTIVARIATE AFFINE FRACTAL INTERPOLATION Article Swipe
M. A. Navascués
,
S. K. Katiyar
,
A. K. B. Chand
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1142/s0218348x20501364
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.1142/s0218348x20501364
Fractal interpolation functions capture the irregularity of some data very effectively in comparison with the classical interpolants. They yield a new technique for fitting experimental data sampled from real world signals, which are usually difficult to represent using the classical approaches. The affine fractal interpolants constitute a generalization of the broken line interpolation, which appears as a particular case of the linear self-affine functions for specific values of the scale parameters. We study the [Formula: see text] convergence of this type of interpolants for [Formula: see text] extending in this way the results available in the literature. In the second part, the affine approximants are defined in higher dimensions via product of interpolation spaces, considering rectangular grids in the product intervals. The associate operator of projection is considered. Some properties of the new functions are established and the aforementioned operator on the space of continuous functions defined on a multidimensional compact rectangle is studied.
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Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1142/s0218348x20501364
- OA Status
- green
- Cited By
- 11
- References
- 24
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3080724354
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W3080724354Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1142/s0218348x20501364Digital Object Identifier
- Title
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MULTIVARIATE AFFINE FRACTAL INTERPOLATIONWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2020Year of publication
- Publication date
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2020-08-22Full publication date if available
- Authors
-
M. A. Navascués, S. K. Katiyar, A. K. B. ChandList of authors in order
- Landing page
-
https://doi.org/10.1142/s0218348x20501364Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
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https://zaguan.unizar.es/record/108583/files/texto_completo.pdfDirect OA link when available
- Concepts
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Mathematics, Affine transformation, Interpolation (computer graphics), Fractal, Linear interpolation, Applied mathematics, Mathematical analysis, Pure mathematics, Computer science, Image (mathematics), Artificial intelligence, PolynomialTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
11Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1, 2024: 1, 2023: 5, 2022: 2, 2021: 2Per-year citation counts (last 5 years)
- References (count)
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24Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.higher | 107 |
| abstract_inverted_index.linear | 61 |
| abstract_inverted_index.second | 99 |
| abstract_inverted_index.values | 66 |
| abstract_inverted_index.Fractal | 0 |
| abstract_inverted_index.appears | 54 |
| abstract_inverted_index.capture | 3 |
| abstract_inverted_index.compact | 150 |
| abstract_inverted_index.defined | 105, 146 |
| abstract_inverted_index.fitting | 23 |
| abstract_inverted_index.fractal | 43 |
| abstract_inverted_index.product | 110, 119 |
| abstract_inverted_index.results | 92 |
| abstract_inverted_index.sampled | 26 |
| abstract_inverted_index.spaces, | 113 |
| abstract_inverted_index.usually | 33 |
| abstract_inverted_index.operator | 123, 139 |
| abstract_inverted_index.signals, | 30 |
| abstract_inverted_index.specific | 65 |
| abstract_inverted_index.studied. | 153 |
| abstract_inverted_index.[Formula: | 74, 84 |
| abstract_inverted_index.associate | 122 |
| abstract_inverted_index.available | 93 |
| abstract_inverted_index.classical | 15, 39 |
| abstract_inverted_index.difficult | 34 |
| abstract_inverted_index.extending | 87 |
| abstract_inverted_index.functions | 2, 63, 133, 145 |
| abstract_inverted_index.rectangle | 151 |
| abstract_inverted_index.represent | 36 |
| abstract_inverted_index.technique | 21 |
| abstract_inverted_index.comparison | 12 |
| abstract_inverted_index.constitute | 45 |
| abstract_inverted_index.continuous | 144 |
| abstract_inverted_index.dimensions | 108 |
| abstract_inverted_index.intervals. | 120 |
| abstract_inverted_index.particular | 57 |
| abstract_inverted_index.projection | 125 |
| abstract_inverted_index.properties | 129 |
| abstract_inverted_index.approaches. | 40 |
| abstract_inverted_index.considered. | 127 |
| abstract_inverted_index.considering | 114 |
| abstract_inverted_index.convergence | 77 |
| abstract_inverted_index.effectively | 10 |
| abstract_inverted_index.established | 135 |
| abstract_inverted_index.literature. | 96 |
| abstract_inverted_index.parameters. | 70 |
| abstract_inverted_index.rectangular | 115 |
| abstract_inverted_index.self-affine | 62 |
| abstract_inverted_index.approximants | 103 |
| abstract_inverted_index.experimental | 24 |
| abstract_inverted_index.interpolants | 44, 82 |
| abstract_inverted_index.irregularity | 5 |
| abstract_inverted_index.interpolants. | 16 |
| abstract_inverted_index.interpolation | 1, 112 |
| abstract_inverted_index.aforementioned | 138 |
| abstract_inverted_index.generalization | 47 |
| abstract_inverted_index.interpolation, | 52 |
| abstract_inverted_index.multidimensional | 149 |
| cited_by_percentile_year.max | 98 |
| cited_by_percentile_year.min | 90 |
| countries_distinct_count | 2 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.94418605 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | True |