Academic Journal
Constructive Approximation of Nonlinear Operators Based on Piecewise Interpolation Technique.
| Τίτλος: | Constructive Approximation of Nonlinear Operators Based on Piecewise Interpolation Technique. |
|---|---|
| Συγγραφείς: | Torokhti, Anatoli1 (AUTHOR) anatoli.torokhti@gmail.com, Pudney, Peter1 (AUTHOR) |
| Πηγή: | Axioms (2075-1680). Feb2026, Vol. 15 Issue 2, p91. 25p. |
| Θεματικοί όροι: | *Nonlinear operators, *Interpolation, *Operator theory, *Approximation theory, *Pseudoinverses, *Mathematical analysis, *Lipschitz continuity, *Random variables |
| Περίληψη: | Suppose K Y and K X are the image and the preimage of a nonlinear operator F : K Y → K X . It is supposed that the cardinality of each K Y and K X is N and N is large. We provide an approximation to the map F that requires prior information only on a few elements p from K Y , where p ≪ N , but still effectively represents F (K Y) . It is achieved under Lipschitz continuity assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of sets of stochastic elements. The proposed technique provides a single operator that transforms any element from the arbitrarily large set K Y . The operator is determined in terms of pseudo-inverse matrices so that it always exists. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://resolver.ebsco.com/c/fiv2js/result?sid=EBSCO:asx&genre=article&issn=20751680&ISBN=&volume=15&issue=2&date=20260201&spage=91&pages=91-115&title=Axioms (2075-1680)&atitle=Constructive%20Approximation%20of%20Nonlinear%20Operators%20Based%20on%20Piecewise%20Interpolation%20Technique.&aulast=Torokhti%2C%20Anatoli&id=DOI:10.3390/axioms15020091 Name: Full Text Finder (for New FTF UI) (ns324271) Category: fullText Text: Full Text Finder MouseOverText: Full Text Finder |
|---|---|
| Header | DbId: asx DbLabel: Academic Search Index An: 192036176 RelevancyScore: 1411 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1411.06896972656 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Constructive Approximation of Nonlinear Operators Based on Piecewise Interpolation Technique. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Torokhti%2C+Anatoli%22">Torokhti, Anatoli</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> anatoli.torokhti@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Pudney%2C+Peter%22">Pudney, Peter</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Axioms+%282075-1680%29%22">Axioms (2075-1680)</searchLink>. Feb2026, Vol. 15 Issue 2, p91. 25p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Nonlinear+operators%22">Nonlinear operators</searchLink><br />*<searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br />*<searchLink fieldCode="DE" term="%22Operator+theory%22">Operator theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Pseudoinverses%22">Pseudoinverses</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+analysis%22">Mathematical analysis</searchLink><br />*<searchLink fieldCode="DE" term="%22Lipschitz+continuity%22">Lipschitz continuity</searchLink><br />*<searchLink fieldCode="DE" term="%22Random+variables%22">Random variables</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Suppose K Y and K X are the image and the preimage of a nonlinear operator F : K Y → K X . It is supposed that the cardinality of each K Y and K X is N and N is large. We provide an approximation to the map F that requires prior information only on a few elements p from K Y , where p ≪ N , but still effectively represents F (K Y) . It is achieved under Lipschitz continuity assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of sets of stochastic elements. The proposed technique provides a single operator that transforms any element from the arbitrarily large set K Y . The operator is determined in terms of pseudo-inverse matrices so that it always exists. [ABSTRACT FROM AUTHOR] |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=192036176 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3390/axioms15020091 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 25 StartPage: 91 Subjects: – SubjectFull: Nonlinear operators Type: general – SubjectFull: Interpolation Type: general – SubjectFull: Operator theory Type: general – SubjectFull: Approximation theory Type: general – SubjectFull: Pseudoinverses Type: general – SubjectFull: Mathematical analysis Type: general – SubjectFull: Lipschitz continuity Type: general – SubjectFull: Random variables Type: general Titles: – TitleFull: Constructive Approximation of Nonlinear Operators Based on Piecewise Interpolation Technique. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Torokhti, Anatoli – PersonEntity: Name: NameFull: Pudney, Peter IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 02 Text: Feb2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 20751680 Numbering: – Type: volume Value: 15 – Type: issue Value: 2 Titles: – TitleFull: Axioms (2075-1680) Type: main |
| ResultId | 1 |