On solving some Cauchy singular integral equations by de la Vallée Poussin filtered approximation
The paper deals with the numerical solution of Cauchy Singular Integral Equations based on some non standard polynomial quasi–projection of de la Vallée Poussin type. Such kind of approximation presents several advantages over classical Lagrange interpolation such as the uniform boundedness of the L...
Saved in:
| Published in | Applied numerical mathematics Vol. 200; pp. 358 - 378 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.06.2024
|
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | The paper deals with the numerical solution of Cauchy Singular Integral Equations based on some non standard polynomial quasi–projection of de la Vallée Poussin type. Such kind of approximation presents several advantages over classical Lagrange interpolation such as the uniform boundedness of the Lebesgue constants, the near–best order of uniform convergence to any continuous function, and a strong reduction of Gibbs phenomenon. These features will be inherited by the proposed numerical method which is stable and convergent, and provides a near-best polynomial approximation of the sought solution by solving a well conditioned linear system. The numerical tests confirm the theoretical error estimates and, in case of functions subject to Gibbs phenomenon, they show a better local approximation compared with analogous Lagrange projection methods. |
|---|---|
| AbstractList | The paper deals with the numerical solution of Cauchy Singular Integral Equations based on some non standard polynomial quasi–projection of de la Vallée Poussin type. Such kind of approximation presents several advantages over classical Lagrange interpolation such as the uniform boundedness of the Lebesgue constants, the near–best order of uniform convergence to any continuous function, and a strong reduction of Gibbs phenomenon. These features will be inherited by the proposed numerical method which is stable and convergent, and provides a near-best polynomial approximation of the sought solution by solving a well conditioned linear system. The numerical tests confirm the theoretical error estimates and, in case of functions subject to Gibbs phenomenon, they show a better local approximation compared with analogous Lagrange projection methods. |
| Author | Themistoclakis, Woula Occorsio, Donatella Russo, Maria Grazia |
| Author_xml | – sequence: 1 givenname: Donatella orcidid: 0000-0001-9446-4452 surname: Occorsio fullname: Occorsio, Donatella email: donatella.occorsio@unibas.it organization: Department of Mathematics, Computer Science and Economics, University of Basilicata, Via dell'Ateneo Lucano 10, 85100 Potenza, Italy – sequence: 2 givenname: Maria Grazia orcidid: 0000-0002-4078-620X surname: Russo fullname: Russo, Maria Grazia email: mariagrazia.russo@unibas.it organization: Department of Mathematics, Computer Science and Economics, University of Basilicata, Via dell'Ateneo Lucano 10, 85100 Potenza, Italy – sequence: 3 givenname: Woula surname: Themistoclakis fullname: Themistoclakis, Woula email: woula.themistoclakis@cnr.it organization: C.N.R. National Research Council of Italy, IAC Institute for Applied Computing “Mauro Picone”, Via P. Castellino, 111, 80131 Napoli, Italy |
| BookMark | eNqFkE1OwzAQhb0oEm3hBGx8gYSxkzTJggWq-JMqlQWwtRx7Uly5TrGTih6Jc3AxTMuKBazeaJ6-0Zs3ISPXOSTkgkHKgM0u16ncumGTcuBZCmUKnI_IODpVUvMyPyWTENYAUBQ5jEmzdDR0dmfcKuoG6VwO6nVPQ1wMVnpqXI8rLy3Ft0H2pnOBNnuqkVpJX6S1nx9IH7shRIC2xvboUVO53fru3WwOwBk5aaUNeP6jU_J8e_M0v08Wy7uH-fUiUVle9UmhAJXmRYkl06xgjap03TQVZFLyvGbQzpSu8qbI2iyPXsmbFvSsAsYrjFM2JfXxrvJdCB5boUx_SNB7aaxgIL4LEmtxKEh8FySgFLGgyGa_2K2P8f3-H-rqSGF8a2fQi6AMOoXaeFS90J35k_8CgsSIHg |
| CitedBy_id | crossref_primary_10_3390_math12172700 crossref_primary_10_1007_s40314_024_02969_z crossref_primary_10_1016_j_apnum_2024_07_004 |
| Cites_doi | 10.1002/mana.200710633 10.1016/j.cam.2004.10.003 10.1216/jiea/1181075986 10.1007/BF01935021 10.1007/s003659900107 10.1016/j.apnum.2021.04.013 10.1007/s00020-002-1289-2 10.1023/A:1006637303487 10.1553/etna_vol58s378 10.1007/BF01203022 10.1007/BF00020079 10.1002/mana.200310121 10.1007/s11075-012-9588-4 10.1016/S0377-0427(00)00482-9 10.1007/s10851-022-01135-6 10.1016/j.cam.2022.114166 10.1007/BF00933186 10.1090/S0002-9939-1988-0969047-5 10.1007/s10444-004-1828-2 10.1007/s11075-016-0194-8 10.1016/S0377-0427(96)00128-8 10.2478/cmam-2011-0029 10.1007/s11075-020-01053-x 10.1016/j.matcom.2017.06.005 10.1016/j.cam.2013.09.063 |
| ContentType | Journal Article |
| Copyright | 2023 The Author(s) |
| Copyright_xml | – notice: 2023 The Author(s) |
| DBID | 6I. AAFTH AAYXX CITATION |
| DOI | 10.1016/j.apnum.2023.07.022 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences |
| EndPage | 378 |
| ExternalDocumentID | 10_1016_j_apnum_2023_07_022 S0168927423002052 |
| GroupedDBID | --K --M -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 23M 4.4 457 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN AAEDT AAEDW AAFTH AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AATTM AAXKI AAXUO AAYWO ABAOU ABEFU ABJNI ABMAC ABWVN ABXDB ACDAQ ACGFS ACRLP ACRPL ADBBV ADEZE ADGUI ADIYS ADMUD ADNMO AEBSH AEIPS AEKER AENEX AFFNX AFJKZ AFTJW AFXIZ AGCQF AGHFR AGQPQ AGRNS AGUBO AGYEJ AHHHB AI. AIEXJ AIGVJ AIKHN AITUG AKRWK ALMA_UNASSIGNED_HOLDINGS AMRAJ ANKPU APXCP ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC BNPGV CS3 EBS EFJIC EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HMJ HVGLF HZ~ IHE J1W KOM M26 M41 MHUIS MO0 N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SME SPC SPCBC SSH SSW SSZ T5K TN5 VH1 VOH WH7 WUQ XPP ZMT ~02 ~G- AAYXX ACVFH ADCNI AEUPX AFPUW AIGII AIIUN AKBMS AKYEP CITATION |
| ID | FETCH-LOGICAL-c348t-5c0ecd257e71d151bc8d9bb803aa24910f6cd84b53f34c8d72bf0d680128ef0d3 |
| IEDL.DBID | .~1 |
| ISSN | 0168-9274 |
| IngestDate | Tue Jul 01 01:13:46 EDT 2025 Thu Apr 24 23:11:39 EDT 2025 Fri May 16 00:29:17 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | De la Vallée Poussin approximation Polynomial approximation Cauchy singular equations Orthogonal polynomials |
| Language | English |
| License | This is an open access article under the CC BY license. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c348t-5c0ecd257e71d151bc8d9bb803aa24910f6cd84b53f34c8d72bf0d680128ef0d3 |
| ORCID | 0000-0002-4078-620X 0000-0001-9446-4452 |
| OpenAccessLink | https://www.sciencedirect.com/science/article/pii/S0168927423002052 |
| PageCount | 21 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_apnum_2023_07_022 crossref_primary_10_1016_j_apnum_2023_07_022 elsevier_sciencedirect_doi_10_1016_j_apnum_2023_07_022 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | June 2024 2024-06-00 |
| PublicationDateYYYYMMDD | 2024-06-01 |
| PublicationDate_xml | – month: 06 year: 2024 text: June 2024 |
| PublicationDecade | 2020 |
| PublicationTitle | Applied numerical mathematics |
| PublicationYear | 2024 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Fromme, Golberg (br0130) 1978; 24 Prössdorf, Silbermann (br0340) 1991; vol. 52 Mastroianni, Russo, Themistoclakis (br0210) 2002; 42 Themistoclakis (br0380) 2018; 147 Capobianco, Russo (br0040) 1997; 9 De Bonis, Mennouni, Occorsio (br0090) 2023 Capobianco, Themistoclakis (br0050) 2001; 7 Almira, Luther (br0010) 2004; 263–264 Muskhelishvili (br0250) 1953 Occorsio, Ramella, Themistoclakis (br0260) 2023; 65 Anderssen, de Hoog, Lukas (br0020) 1980 Occorsio, Themistoclakis (br0300) 2020; 385 De Bonis, Mastroianni (br0080) 2011; 2 De Bonis (br0070) 2014; 260 Occorsio, Russo, Themistoclakis (br0270) 2022; 410 Parton, Perlin (br0330) 1982 Themistoclakis, Filbir (br0400) 2008; 281 Occorsio, Themistoclakis (br0290) 2020; vol. 11973 Ditzian, Totik (br0120) 1988; 104 Mastroianni, Themistoclakis (br0230) 2005; 180 Luther (br0180) 2005; 52 Themistoclakis (br0370) 2012; 60 Junghanns, Luther (br0150) 1997; 77 Mikhlin, Prössdorf (br0240) 1986 Themistoclakis (br0360) 1999; 84 Golberg (br0140) 1979 Occorsio, Themistoclakis (br0310) 2021; 166 Ditzian, Totik (br0110) 1987 Mastroianni, Russo, Themistoclakis (br0220) 2005; vol. 160 Mastroianni, Prössdorf (br0190) 1994; 34 Occorsio, Themistoclakis (br0320) 2021; 14 Occorsio, Russo, Themistoclakis (br0280) 2022; 15 Themistoclakis, Filbir (br0390) 2004; 6 Junghanns, Silbermann (br0160) 2000; 125 Kurtz, Farris, Sun (br0170) 1994; 66 Atkinson (br0030) 1997; vol. 552 De Bonis, Occorsio, Themistoclakis (br0100) 2021 Mastroianni, Russo (br0200) 1999; 15 Capobianco, Themistoclakis (br0060) 2004; 23 Sloan (br0350) 2011; 11 Themistoclakis, Van Barel (br0410) 2017; 75 Capobianco (10.1016/j.apnum.2023.07.022_br0060) 2004; 23 Themistoclakis (10.1016/j.apnum.2023.07.022_br0400) 2008; 281 Junghanns (10.1016/j.apnum.2023.07.022_br0150) 1997; 77 Anderssen (10.1016/j.apnum.2023.07.022_br0020) 1980 Mikhlin (10.1016/j.apnum.2023.07.022_br0240) 1986 Occorsio (10.1016/j.apnum.2023.07.022_br0310) 2021; 166 Mastroianni (10.1016/j.apnum.2023.07.022_br0220) 2005; vol. 160 Occorsio (10.1016/j.apnum.2023.07.022_br0280) 2022; 15 Mastroianni (10.1016/j.apnum.2023.07.022_br0190) 1994; 34 Capobianco (10.1016/j.apnum.2023.07.022_br0040) 1997; 9 Mastroianni (10.1016/j.apnum.2023.07.022_br0200) 1999; 15 Mastroianni (10.1016/j.apnum.2023.07.022_br0210) 2002; 42 Prössdorf (10.1016/j.apnum.2023.07.022_br0340) 1991; vol. 52 Almira (10.1016/j.apnum.2023.07.022_br0010) 2004; 263–264 De Bonis (10.1016/j.apnum.2023.07.022_br0070) 2014; 260 De Bonis (10.1016/j.apnum.2023.07.022_br0080) 2011; 2 Mastroianni (10.1016/j.apnum.2023.07.022_br0230) 2005; 180 Muskhelishvili (10.1016/j.apnum.2023.07.022_br0250) 1953 Themistoclakis (10.1016/j.apnum.2023.07.022_br0360) 1999; 84 Ditzian (10.1016/j.apnum.2023.07.022_br0110) 1987 Occorsio (10.1016/j.apnum.2023.07.022_br0300) 2020; 385 Junghanns (10.1016/j.apnum.2023.07.022_br0160) 2000; 125 Capobianco (10.1016/j.apnum.2023.07.022_br0050) 2001; 7 De Bonis (10.1016/j.apnum.2023.07.022_br0100) 2021 Themistoclakis (10.1016/j.apnum.2023.07.022_br0410) 2017; 75 Ditzian (10.1016/j.apnum.2023.07.022_br0120) 1988; 104 Golberg (10.1016/j.apnum.2023.07.022_br0140) 1979 Kurtz (10.1016/j.apnum.2023.07.022_br0170) 1994; 66 Luther (10.1016/j.apnum.2023.07.022_br0180) 2005; 52 Themistoclakis (10.1016/j.apnum.2023.07.022_br0390) 2004; 6 Occorsio (10.1016/j.apnum.2023.07.022_br0260) 2023; 65 Themistoclakis (10.1016/j.apnum.2023.07.022_br0380) 2018; 147 Fromme (10.1016/j.apnum.2023.07.022_br0130) 1978; 24 De Bonis (10.1016/j.apnum.2023.07.022_br0090) 2023 Themistoclakis (10.1016/j.apnum.2023.07.022_br0370) 2012; 60 Occorsio (10.1016/j.apnum.2023.07.022_br0270) 2022; 410 Parton (10.1016/j.apnum.2023.07.022_br0330) 1982 Occorsio (10.1016/j.apnum.2023.07.022_br0290) 2020; vol. 11973 Sloan (10.1016/j.apnum.2023.07.022_br0350) 2011; 11 Atkinson (10.1016/j.apnum.2023.07.022_br0030) 1997; vol. 552 Occorsio (10.1016/j.apnum.2023.07.022_br0320) 2021; 14 |
| References_xml | – year: 1979 ident: br0140 article-title: Solution Methods for Integral Equations: Theory and Applications – year: 1987 ident: br0110 article-title: Moduli of Smoothness – volume: 14 start-page: 68 year: 2021 end-page: 84 ident: br0320 article-title: Some remarks on filtered polynomial interpolation at Chebyshev nodes publication-title: Dolomites Res. Notes Approx. – volume: vol. 52 year: 1991 ident: br0340 article-title: Numerical Analysis for Integral and Related Operator Equations publication-title: Operator Theory: Advances and Applications – year: 1953 ident: br0250 article-title: Singular Integral Equations – volume: 11 start-page: 540 year: 2011 end-page: 552 ident: br0350 article-title: Polynomial approximation on spheres: generalizing de la Vallée Poussin publication-title: Comput. Methods Appl. Math. – year: 1980 ident: br0020 article-title: The Application and Numerical Solution of Integral Equations – volume: 263–264 start-page: 3 year: 2004 end-page: 35 ident: br0010 article-title: Generalized approximation spaces and applications publication-title: Math. Nachr. – year: 1986 ident: br0240 article-title: Singular Integral Operators – volume: 9 start-page: 21 year: 1997 end-page: 45 ident: br0040 article-title: Uniform convergence estimates for a collocation method for the Cauchy singular integral equation publication-title: J. Integral Equ. Appl. – volume: 77 start-page: 201 year: 1997 end-page: 237 ident: br0150 article-title: Cauchy singular integral equations in spaces of continuous functions and methods for their numerical solution publication-title: J. Comput. Appl. Math. – volume: 75 start-page: 1 year: 2017 end-page: 31 ident: br0410 article-title: Generalized de la Vallée Poussin approximations on [−1, 1] publication-title: Numer. Algorithms – volume: 7 start-page: 417 year: 2001 end-page: 444 ident: br0050 article-title: On the boundedness of de la Vallée Poussin operators publication-title: East J. Approx. – volume: 52 start-page: 527 year: 2005 end-page: 560 ident: br0180 article-title: Cauchy singular integral operators in weighted spaces of continuous functions publication-title: Integral Equ. Oper. Theory – volume: 260 start-page: 117 year: 2014 end-page: 134 ident: br0070 article-title: Remarks on two integral operators and numerical methods for CSIE publication-title: J. Comput. Appl. Math. – volume: 42 start-page: 57 year: 2002 end-page: 89 ident: br0210 article-title: The boundedness of the Cauchy singular integral operator in weighted Besov type spaces with uniform norms publication-title: Integral Equ. Oper. Theory – volume: 24 start-page: 169 year: 1978 end-page: 206 ident: br0130 article-title: Numerical solution of a class of integral equations arising in two-dimensional aerodynamics publication-title: J. Optim. Theory Appl. – volume: 104 start-page: 1059 year: 1988 end-page: 1066 ident: br0120 article-title: Remarks on Besov spaces and best polynomial approximation publication-title: Proc. Am. Math. Soc. – volume: vol. 552 year: 1997 ident: br0030 article-title: The Numerical Solution of Integral Equations of the Second Kind publication-title: Cambridge Monographs on Applied and Computational Mathematics – volume: 84 year: 1999 ident: br0360 article-title: Some interpolating operators of de la Vallée Poussin type publication-title: Acta Math. Hung. – year: 2021 ident: br0100 article-title: Filtered interpolation for solving Prandtl's integro-differential equations publication-title: Numer. Algorithms – year: 2023 ident: br0090 article-title: A numerical method for solving systems of hypersingular integro-differential equations publication-title: Electron. Trans. Numer. Anal. – volume: 15 start-page: 93 year: 2022 end-page: 104 ident: br0280 article-title: Filtered integration rules for finite weighted Hilbert transforms II publication-title: Dolomites Res. Notes Approx. – volume: 34 start-page: 120 year: 1994 end-page: 128 ident: br0190 article-title: Some nodes matrices appearing in the numerical analysis for singular integral equations publication-title: BIT – volume: 166 start-page: 272 year: 2021 end-page: 287 ident: br0310 article-title: On the filtered polynomial interpolation at Chebyshev nodes publication-title: Appl. Numer. Math. – volume: 60 start-page: 593 year: 2012 end-page: 612 ident: br0370 article-title: Uniform approximation on [−1, 1] via discrete de la Vallée Poussin means publication-title: Numer. Algorithms – volume: 180 start-page: 71 year: 2005 end-page: 105 ident: br0230 article-title: A numerical method for the generalized airfoil equation based on the de la Vallée Poussin interpolation publication-title: J. Comput. Appl. Math. – volume: 23 start-page: 353 year: 2004 end-page: 374 ident: br0060 article-title: Interpolating polynomial wavelets on [-1, 1] publication-title: Adv. Comput. Math. – volume: 15 start-page: 257 year: 1999 end-page: 289 ident: br0200 article-title: Lagrange interpolation in weighted Besov spaces publication-title: Constr. Approx. – year: 1982 ident: br0330 article-title: Integral Equations in Elasticity – volume: 65 start-page: 513 year: 2023 end-page: 541 ident: br0260 article-title: Image scaling by de la Vallée Poussin filtered interpolation publication-title: J. Math. Imaging Vis. – volume: 385 year: 2020 ident: br0300 article-title: Uniform weighted approximation on the square by polynomial interpolation at Chebyshev nodes publication-title: Appl. Math. Comput. – volume: 147 start-page: 279 year: 2018 end-page: 292 ident: br0380 article-title: Weighted publication-title: Math. Comput. Simul. – volume: 6 start-page: 297 year: 2004 end-page: 312 ident: br0390 article-title: On the construction of de la Vallée Poussin means for orthogonal polynomials using convolution structures publication-title: J. Comput. Anal. Appl. – volume: 125 start-page: 395 year: 2000 end-page: 421 ident: br0160 article-title: Numerical analysis for one-dimensional Cauchy singular integral equations publication-title: J. Comput. Appl. Math. – volume: 281 start-page: 650 year: 2008 end-page: 668 ident: br0400 article-title: Polynomial approximation on the sphere using scattered data publication-title: Math. Nachr. – volume: 2 start-page: 29 year: 2011 end-page: 55 ident: br0080 article-title: Direct methods for CSIE in weighted Zygmund spaces with uniform norm publication-title: Riv. Mat. Univ. Parma – volume: 410 start-page: 29 year: 2022 ident: br0270 article-title: Filtered integration rules for finite weighted Hilbert transforms publication-title: J. Comput. Appl. Math. – volume: vol. 11973 start-page: 86 year: 2020 end-page: 100 ident: br0290 article-title: Uniform weighted approximation by multivariate filtered polynomials publication-title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) – volume: 66 start-page: 139 year: 1994 end-page: 154 ident: br0170 article-title: The numerical solution of Cauchy singular integral equations with application to fracture publication-title: Int. J. Fract. – volume: vol. 160 start-page: 311 year: 2005 end-page: 336 ident: br0220 article-title: Numerical methods for Cauchy singular integral equations in spaces of weighted continuous functions publication-title: Recent Advances in Operator Theory and Its Applications – volume: 281 start-page: 650 issue: 5 year: 2008 ident: 10.1016/j.apnum.2023.07.022_br0400 article-title: Polynomial approximation on the sphere using scattered data publication-title: Math. Nachr. doi: 10.1002/mana.200710633 – volume: 180 start-page: 71 year: 2005 ident: 10.1016/j.apnum.2023.07.022_br0230 article-title: A numerical method for the generalized airfoil equation based on the de la Vallée Poussin interpolation publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2004.10.003 – volume: 9 start-page: 21 year: 1997 ident: 10.1016/j.apnum.2023.07.022_br0040 article-title: Uniform convergence estimates for a collocation method for the Cauchy singular integral equation publication-title: J. Integral Equ. Appl. doi: 10.1216/jiea/1181075986 – year: 1982 ident: 10.1016/j.apnum.2023.07.022_br0330 – volume: 6 start-page: 297 issue: 4 year: 2004 ident: 10.1016/j.apnum.2023.07.022_br0390 article-title: On the construction of de la Vallée Poussin means for orthogonal polynomials using convolution structures publication-title: J. Comput. Anal. Appl. – volume: vol. 11973 start-page: 86 year: 2020 ident: 10.1016/j.apnum.2023.07.022_br0290 article-title: Uniform weighted approximation by multivariate filtered polynomials – volume: 34 start-page: 120 year: 1994 ident: 10.1016/j.apnum.2023.07.022_br0190 article-title: Some nodes matrices appearing in the numerical analysis for singular integral equations publication-title: BIT doi: 10.1007/BF01935021 – year: 1980 ident: 10.1016/j.apnum.2023.07.022_br0020 – volume: vol. 552 year: 1997 ident: 10.1016/j.apnum.2023.07.022_br0030 article-title: The Numerical Solution of Integral Equations of the Second Kind – volume: 15 start-page: 257 year: 1999 ident: 10.1016/j.apnum.2023.07.022_br0200 article-title: Lagrange interpolation in weighted Besov spaces publication-title: Constr. Approx. doi: 10.1007/s003659900107 – volume: 166 start-page: 272 year: 2021 ident: 10.1016/j.apnum.2023.07.022_br0310 article-title: On the filtered polynomial interpolation at Chebyshev nodes publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2021.04.013 – volume: 52 start-page: 527 issue: 4 year: 2005 ident: 10.1016/j.apnum.2023.07.022_br0180 article-title: Cauchy singular integral operators in weighted spaces of continuous functions publication-title: Integral Equ. Oper. Theory doi: 10.1007/s00020-002-1289-2 – volume: 84 issue: 3 year: 1999 ident: 10.1016/j.apnum.2023.07.022_br0360 article-title: Some interpolating operators of de la Vallée Poussin type publication-title: Acta Math. Hung. doi: 10.1023/A:1006637303487 – volume: 14 start-page: 68 issue: 2 year: 2021 ident: 10.1016/j.apnum.2023.07.022_br0320 article-title: Some remarks on filtered polynomial interpolation at Chebyshev nodes publication-title: Dolomites Res. Notes Approx. – year: 2023 ident: 10.1016/j.apnum.2023.07.022_br0090 article-title: A numerical method for solving systems of hypersingular integro-differential equations publication-title: Electron. Trans. Numer. Anal. doi: 10.1553/etna_vol58s378 – volume: 42 start-page: 57 issue: 1 year: 2002 ident: 10.1016/j.apnum.2023.07.022_br0210 article-title: The boundedness of the Cauchy singular integral operator in weighted Besov type spaces with uniform norms publication-title: Integral Equ. Oper. Theory doi: 10.1007/BF01203022 – volume: 66 start-page: 139 issue: 2 year: 1994 ident: 10.1016/j.apnum.2023.07.022_br0170 article-title: The numerical solution of Cauchy singular integral equations with application to fracture publication-title: Int. J. Fract. doi: 10.1007/BF00020079 – volume: 263–264 start-page: 3 year: 2004 ident: 10.1016/j.apnum.2023.07.022_br0010 article-title: Generalized approximation spaces and applications publication-title: Math. Nachr. doi: 10.1002/mana.200310121 – year: 1979 ident: 10.1016/j.apnum.2023.07.022_br0140 – volume: 60 start-page: 593 issue: 4 year: 2012 ident: 10.1016/j.apnum.2023.07.022_br0370 article-title: Uniform approximation on [−1, 1] via discrete de la Vallée Poussin means publication-title: Numer. Algorithms doi: 10.1007/s11075-012-9588-4 – volume: 15 start-page: 93 issue: 3 year: 2022 ident: 10.1016/j.apnum.2023.07.022_br0280 article-title: Filtered integration rules for finite weighted Hilbert transforms II publication-title: Dolomites Res. Notes Approx. – volume: 125 start-page: 395 issue: 1 year: 2000 ident: 10.1016/j.apnum.2023.07.022_br0160 article-title: Numerical analysis for one-dimensional Cauchy singular integral equations publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(00)00482-9 – year: 1986 ident: 10.1016/j.apnum.2023.07.022_br0240 – volume: 65 start-page: 513 issue: 3 year: 2023 ident: 10.1016/j.apnum.2023.07.022_br0260 article-title: Image scaling by de la Vallée Poussin filtered interpolation publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-022-01135-6 – volume: 410 start-page: 29 year: 2022 ident: 10.1016/j.apnum.2023.07.022_br0270 article-title: Filtered integration rules for finite weighted Hilbert transforms publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2022.114166 – year: 1953 ident: 10.1016/j.apnum.2023.07.022_br0250 – volume: 2 start-page: 29 year: 2011 ident: 10.1016/j.apnum.2023.07.022_br0080 article-title: Direct methods for CSIE in weighted Zygmund spaces with uniform norm publication-title: Riv. Mat. Univ. Parma – year: 1987 ident: 10.1016/j.apnum.2023.07.022_br0110 – volume: vol. 160 start-page: 311 year: 2005 ident: 10.1016/j.apnum.2023.07.022_br0220 article-title: Numerical methods for Cauchy singular integral equations in spaces of weighted continuous functions – volume: vol. 52 year: 1991 ident: 10.1016/j.apnum.2023.07.022_br0340 article-title: Numerical Analysis for Integral and Related Operator Equations – volume: 24 start-page: 169 issue: 1 year: 1978 ident: 10.1016/j.apnum.2023.07.022_br0130 article-title: Numerical solution of a class of integral equations arising in two-dimensional aerodynamics publication-title: J. Optim. Theory Appl. doi: 10.1007/BF00933186 – volume: 104 start-page: 1059 year: 1988 ident: 10.1016/j.apnum.2023.07.022_br0120 article-title: Remarks on Besov spaces and best polynomial approximation publication-title: Proc. Am. Math. Soc. doi: 10.1090/S0002-9939-1988-0969047-5 – volume: 23 start-page: 353 year: 2004 ident: 10.1016/j.apnum.2023.07.022_br0060 article-title: Interpolating polynomial wavelets on [-1, 1] publication-title: Adv. Comput. Math. doi: 10.1007/s10444-004-1828-2 – volume: 75 start-page: 1 issue: 1 year: 2017 ident: 10.1016/j.apnum.2023.07.022_br0410 article-title: Generalized de la Vallée Poussin approximations on [−1, 1] publication-title: Numer. Algorithms doi: 10.1007/s11075-016-0194-8 – volume: 385 year: 2020 ident: 10.1016/j.apnum.2023.07.022_br0300 article-title: Uniform weighted approximation on the square by polynomial interpolation at Chebyshev nodes publication-title: Appl. Math. Comput. – volume: 77 start-page: 201 issue: 1-2 year: 1997 ident: 10.1016/j.apnum.2023.07.022_br0150 article-title: Cauchy singular integral equations in spaces of continuous functions and methods for their numerical solution publication-title: J. Comput. Appl. Math. doi: 10.1016/S0377-0427(96)00128-8 – volume: 11 start-page: 540 issue: 4 year: 2011 ident: 10.1016/j.apnum.2023.07.022_br0350 article-title: Polynomial approximation on spheres: generalizing de la Vallée Poussin publication-title: Comput. Methods Appl. Math. doi: 10.2478/cmam-2011-0029 – year: 2021 ident: 10.1016/j.apnum.2023.07.022_br0100 article-title: Filtered interpolation for solving Prandtl's integro-differential equations publication-title: Numer. Algorithms doi: 10.1007/s11075-020-01053-x – volume: 147 start-page: 279 year: 2018 ident: 10.1016/j.apnum.2023.07.022_br0380 article-title: Weighted L1 approximation on [−1, 1] via discrete de la Vallée Poussin means publication-title: Math. Comput. Simul. doi: 10.1016/j.matcom.2017.06.005 – volume: 7 start-page: 417 issue: 4 year: 2001 ident: 10.1016/j.apnum.2023.07.022_br0050 article-title: On the boundedness of de la Vallée Poussin operators publication-title: East J. Approx. – volume: 260 start-page: 117 year: 2014 ident: 10.1016/j.apnum.2023.07.022_br0070 article-title: Remarks on two integral operators and numerical methods for CSIE publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2013.09.063 |
| SSID | ssj0005540 |
| Score | 2.402567 |
| Snippet | The paper deals with the numerical solution of Cauchy Singular Integral Equations based on some non standard polynomial quasi–projection of de la Vallée... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 358 |
| SubjectTerms | Cauchy singular equations De la Vallée Poussin approximation Orthogonal polynomials Polynomial approximation |
| Title | On solving some Cauchy singular integral equations by de la Vallée Poussin filtered approximation |
| URI | https://dx.doi.org/10.1016/j.apnum.2023.07.022 |
| Volume | 200 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwELWqcuHCjihL5QNHQtPYWXqsKqoCoiBBUW-Rt4igkBbaSPTC__Ad_Bgex0FFQj1wymZH0WQ8iz3vGaFTooMEwJA4RHkAyUmUw4LQdZgvlHS9hHEJQOGbYTAY0auxP66hXoWFgbJKa_tLm26stb3TstJsTdO0da-DlahjVhoh5vHBDlMagpaffyyVefgGFAmNHWhdMQ-ZGi82zQuAo3vEMHh63t_eacnj9LfQhg0Vcbf8mm1UU_kO2rRhI7aDcraL-G2OtQbBzIA-vijcY4V4WmCYBYAiU2wpITKsXkti7xnmCywVzhh-ZFn29anw3aTQoyPHSQrL5_r9hmz8PS2RjXto1L946A0cu3WCIwiN5o4vXCWkHo4qbEvt1LmIZIfzyCWM6YSr7SaBkBHlPkkI1c9CjyeuDIy7UvqM7KN6PsnVAcKcBzrlCXgYMpdSzjttERDJIHcjgvOwgbxKZLGwvOKwvUUWVwVkz7GRcwxyjt0w1nJuoLOfTtOSVmN186D6F_Ev7Yi14V_V8fC_HY_Qur6iZVHYMarP3wp1osOPOW8a_Wqite7l9WD4DdA83OA |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3JTsMwELWq9gAXdkRZfeBI1DTO1mNVUaV0AYkW9WZ5iygKaaGtRD-J7-DHGCcOi4R64JQo9kTRxJ7FnveM0CWBIEFjSCyiHA3JiZXF_MC2mCeUtJ2YcamBwv2BH43cm7E3LqFWgYXRZZXG9uc2PbPW5knNaLM2m0xq9xCshI1sp1HHPB7Y4Ypmp_LKqNLsdKPBd6WHl-EidX9LCxTkQ1mZF5ulS41Id0hG4uk4fzuoH06nvYO2TLSIm_kH7aKSSvfQtokcsZmX833Eb1MMg0gvDsD1WeEWW4rHFdYLAbrOFBtWiASrl5zbe475CkuFE4YfWJJ8vCt8N13CBElxPNE76PD-jG_8bZKDGw_QqH09bEWWOT3BEsQNF5YnbCUkzEgV1CX4dS5C2eA8tAljkHPV7dgXMnS5R2LiQlvg8NiWfuaxFNyRQ1ROp6k6QphzH7IenwcBs12X80Zd-EQynb4RwXlQRU6hMioMtbg-4SKhRQ3ZE830TLWeqR1Q0HMVXX0JzXJmjfXd_eJf0F8DhILtXyd4_F_BC7QRDfs92usMuidoE1rcvEbsFJUXr0t1BtHIgp-b0fYJZ-7fkQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+solving+some+Cauchy+singular+integral+equations+by+de+la+Vall%C3%A9e+Poussin+filtered+approximation&rft.jtitle=Applied+numerical+mathematics&rft.au=Occorsio%2C+Donatella&rft.au=Russo%2C+Maria+Grazia&rft.au=Themistoclakis%2C+Woula&rft.date=2024-06-01&rft.pub=Elsevier+B.V&rft.issn=0168-9274&rft.volume=200&rft.spage=358&rft.epage=378&rft_id=info:doi/10.1016%2Fj.apnum.2023.07.022&rft.externalDocID=S0168927423002052 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0168-9274&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0168-9274&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0168-9274&client=summon |