Asymptotic spectra of large (grid) graphs with a uniform local structure, Part II: Numerical applications
In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain Ω⊂Rd, d≥1. When Ω=[0,1], such graphs include the standard Toeplitz graphs and, for Ω=[0,1]d, the considered class includes d-level Toeplitz graphs. In the general...
Uloženo v:
| Vydáno v: | Journal of computational and applied mathematics Ročník 437; s. 115461 |
|---|---|
| Hlavní autoři: | , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.02.2024
|
| Témata: | |
| ISSN: | 0377-0427, 1879-1778, 1879-1778 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain Ω⊂Rd, d≥1. When Ω=[0,1], such graphs include the standard Toeplitz graphs and, for Ω=[0,1]d, the considered class includes d-level Toeplitz graphs. In the general case, the underlying sequence of adjacency matrices has a canonical eigenvalue distribution, in the Weyl sense, and it has been shown in the theoretical part of this work that we can associate to it a symbol f. The knowledge of the symbol and of its basic analytical features provides key information on the eigenvalue structure in terms of localization, spectral gap, clustering, and global distribution. In the present paper, many different applications are discussed and various numerical examples are presented in order to underline the practical use of the developed theory. Tests and applications are mainly obtained from the approximation of differential operators via numerical schemes such as Finite Differences, Finite Elements, and Isogeometric Analysis. Moreover, we show that more applications can be taken into account, since the results presented here can be applied as well to study the spectral properties of adjacency matrices and Laplacian operators of general large graphs and networks, whenever the involved matrices enjoy a uniform local structure. |
|---|---|
| AbstractList | In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain Ω⊂Rd, d≥1. When Ω=[0,1], such graphs include the standard Toeplitz graphs and, for Ω=[0,1]d, the considered class includes d-level Toeplitz graphs. In the general case, the underlying sequence of adjacency matrices has a canonical eigenvalue distribution, in the Weyl sense, and it has been shown in the theoretical part of this work that we can associate to it a symbol f. The knowledge of the symbol and of its basic analytical features provides key information on the eigenvalue structure in terms of localization, spectral gap, clustering, and global distribution. In the present paper, many different applications are discussed and various numerical examples are presented in order to underline the practical use of the developed theory. Tests and applications are mainly obtained from the approximation of differential operators via numerical schemes such as Finite Differences, Finite Elements, and Isogeometric Analysis. Moreover, we show that more applications can be taken into account, since the results presented here can be applied as well to study the spectral properties of adjacency matrices and Laplacian operators of general large graphs and networks, whenever the involved matrices enjoy a uniform local structure. In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain Ω ⊂ R d , d ≥ 1. When Ω = [0, 1], such graphs include the standard Toeplitz graphs and, for Ω = [0,1] d , the considered class includes d -level Toeplitz graphs. In the general case, the underlying sequence of adjacency matrices has a canonical eigenvalue distribution, in the Weyl sense, and it has been shown in the theoretical part of this work that we can associate to it a symbol f . The knowledge of the symbol and of its basic analytical features provides key information on the eigenvalue structure in terms of localization, spectral gap, clustering, and global distribution. In the present paper, many different applications are discussed and various numerical examples are presented in order to underline the practical use of the developed theory. Tests and applications are mainly obtained from the approximation of differential operators via numerical schemes such as Finite Differences, Finite Elements, and Isogeometric Analysis. Moreover, we show that more applications can be taken into account, since the results presented here can be applied as well to study the spectral properties of adjacency matrices and Laplacian operators of general large graphs and networks, whenever the involved matrices enjoy a uniform local structure. |
| ArticleNumber | 115461 |
| Author | Bianchi, Davide Ferrari, Paola Serra-Capizzano, Stefano Adriani, Andrea |
| Author_xml | – sequence: 1 givenname: Andrea orcidid: 0000-0003-3390-7891 surname: Adriani fullname: Adriani, Andrea email: andrea.adriani@uninsubria.it organization: Department of Theoretical and Applied Sciences, University of Insubria, Via Dunant 3, 21100 Varese, Italy – sequence: 2 givenname: Davide orcidid: 0000-0003-0635-0637 surname: Bianchi fullname: Bianchi, Davide email: bianchi@hit.edu.cn organization: School of Science, Harbin Institute of Technology, Shenzhen, University Town of Shenzhen, 518055 Shenzhen, China – sequence: 3 givenname: Paola orcidid: 0000-0001-6615-7404 surname: Ferrari fullname: Ferrari, Paola email: ferrari@uni-wuppertal.de organization: School of Mathematics and Natural Sciences, University of Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany – sequence: 4 givenname: Stefano orcidid: 0000-0001-9477-109X surname: Serra-Capizzano fullname: Serra-Capizzano, Stefano email: stefano.serrac@uninsubria.it, stefano.serra@it.uu.se organization: Department of Science and High Technology, University of Insubria, Via Valleggio 11, 22100 Como, Italy |
| BackLink | https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-509946$$DView record from Swedish Publication Index (Uppsala universitet) |
| BookMark | eNp9kD1PwzAQhi0EEi3wA9g8gtQUO3FiB6aqfFWqgAFYLefiFFdJHNkOFf-elMLC0OlOuve5Oz1jdNjaViN0TsmUEppdraegmmlM4mRKacoyeoBGVPA8opyLQzQiCecRYTE_RmPv14SQLKdshMzMfzVdsMEA9p2G4BS2Fa6VW2l8sXKmvMQrp7oPjzcmfGCF-9ZU1jW4tqBq7IPrIfROT_CLcgEvFtf4qW-0M9up6rp6aIKxrT9FR5WqvT77rSfo7f7udf4YLZ8fFvPZMoIkYSHiPBYZqdJSMKYopAWkGVS0KpVIdE5FnEMBcUkJCC7SgsVABkAwkTKlyoImJ2iy2-s3uusL2TnTKPclrTLy1rzPpHUr2fcyJXnOsiHOd3Fw1nunKwkm_Hw8qDC1pERuBcu1HATLrWC5EzyQ9B_5d2ofc7Nj9GDg02gnPRjdgi6NG-TL0po99DdyE5YA |
| CitedBy_id | crossref_primary_10_1007_s00032_020_00319_2 |
| Cites_doi | 10.1007/s10092-013-0081-9 10.1016/j.exmath.2021.10.004 10.1007/s10543-011-0356-y 10.3390/axioms7030049 10.1553/etna_vol53s28 10.1007/s002110100331 10.1090/S0002-9939-1981-0589143-8 10.1007/BF02575816 10.1016/j.laa.2011.11.032 10.1007/s00032-020-00319-2 10.1016/j.laa.2006.04.012 10.1016/S0024-3795(97)80001-8 10.1007/s10092-021-00426-5 10.1007/s10543-021-00896-7 10.1137/S0895479803421987 10.1007/s00526-022-02249-w 10.1002/nla.2356 10.1080/03081089808818584 10.1007/s10092-018-0288-x 10.1016/S0024-3795(02)00504-9 10.1137/17M115164X 10.1553/etna_vol53s113 10.1016/0898-1221(93)90297-9 10.1007/s00791-015-0253-z 10.1016/S0024-3795(97)10079-9 10.1137/140988590 10.1137/110843563 10.1016/j.cma.2014.06.001 10.1109/ICCSA54496.2021.00023 10.1137/140976480 |
| ContentType | Journal Article |
| Copyright | 2023 Elsevier B.V. |
| Copyright_xml | – notice: 2023 Elsevier B.V. |
| DBID | AAYXX CITATION ADTPV AOWAS DF2 |
| DOI | 10.1016/j.cam.2023.115461 |
| DatabaseName | CrossRef SwePub SwePub Articles SWEPUB Uppsala universitet |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1879-1778 |
| ExternalDocumentID | oai_DiVA_org_uu_509946 10_1016_j_cam_2023_115461 S0377042723004053 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29K 4.4 457 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAFWJ AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABJNI ABMAC ABTAH ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 D-I DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA HVGLF HZ~ IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A NCXOZ NHB O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K TN5 UPT WUQ XPP YQT ZMT ZY4 ~02 ~G- 9DU AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD ADTPV AOWAS DF2 |
| ID | FETCH-LOGICAL-c334t-772860f5d844a1c5bc56cf1fda83e91829cbc2d10c8785b42c028684854aadb13 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001066522800001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0377-0427 1879-1778 |
| IngestDate | Tue Nov 04 16:31:35 EST 2025 Tue Nov 18 21:33:56 EST 2025 Sat Nov 29 07:22:12 EST 2025 Fri Feb 23 02:35:11 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Graph Laplacian 05C22 05C50 Multigrid methods 65J10 15A06 Graphs Asymptotic spectra 65M55 PDE discretizations 65N22 Preconditioning |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c334t-772860f5d844a1c5bc56cf1fda83e91829cbc2d10c8785b42c028684854aadb13 |
| ORCID | 0000-0001-9477-109X 0000-0003-0635-0637 0000-0001-6615-7404 0000-0003-3390-7891 |
| ParticipantIDs | swepub_primary_oai_DiVA_org_uu_509946 crossref_citationtrail_10_1016_j_cam_2023_115461 crossref_primary_10_1016_j_cam_2023_115461 elsevier_sciencedirect_doi_10_1016_j_cam_2023_115461 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-02-01 |
| PublicationDateYYYYMMDD | 2024-02-01 |
| PublicationDate_xml | – month: 02 year: 2024 text: 2024-02-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of computational and applied mathematics |
| PublicationYear | 2024 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Strikwerda (b22) 1989 Keller, Lenz, Wojciechowski (b24) 2021 Serra-Capizzano (b8) 2003; 366 Barbarino, Garoni, Serra-Capizzano (b18) 2020; 53 Brosowski, Deutsch (b40) 1981; 81 D. Bianchi, M. Donatelli, Graph approximation and generalized Tikhonov regularization for signal deblurring, in: Proceedings in IEEE International Conference on Computational Science and Its Applications, 2021, pp. 93–100. Fiorentino, Serra-Capizzano (b29) 1991; 28 Hossein Ghorban (b2) 2012; 1 Böttcher, Silbermann (b3) 1999 Oosterlee, Schüller, Trottenberg (b31) 2001 Di Benedetto, Fiorentino, Serra-Capizzano (b34) 1993; 25 Tilli (b10) 1998; 278 Ruge, Stüben (b25) 1987 Saad (b30) 2003 Tyrtyshnikov, Zamarashkin (b7) 1998; 270 Aricò, Donatelli, Serra-Capizzano (b26) 2004; 26 Donatelli, Serra-Capizzano, Sesana (b28) 2012; 52 Bianchi, Setti, Wojciechowski (b42) 2022; 61 Adriani, Bianchi, Serra-Capizzano (b1) 2020; 88 Garoni, Serra-Capizzano (b15) 2017 Lund, Bowers (b39) 1992 Cottrell, Hughes, Bazilevs (b21) 2009 Garoni, Serra-Capizzano, Sesana (b23) 2015; 36 Cvetkovic, Doob, Sachs (b33) 1979 Grenander, Szegö (b4) 1984 Garoni, Serra-Capizzano (b16) 2018 Ekström, Furci, Garoni, Manni, Serra-Capizzano, Speleers (b38) 2018; 25 Barbarino (b45) 2022; 62 Livne, Brandt (b47) 2012; 34 Donatelli, Ferrari, Furci, Serra-Capizzano, Sesana (b27) 2021; 28 Barbarino, Garoni, Serra-Capizzano (b17) 2020; 53 Garoni, Mazza, Serra-Capizzano (b14) 2018; 7 Donatelli, Garoni, Manni, Serra-Capizzano, Speleers (b37) 2017; 55 Davies (b41) 1996 Bianchi, Serra-Capizzano (b12) 2018; 55 Estrada (b43) 2012; 436 Serra-Capizzano (b9) 2006; 419 Donatelli, Garoni, Manni, Serra-Capizzano, Speleers (b35) 2015; 284 Garoni, Serra-Capizzano, Sesana (b19) 2018 Donatelli, Mazza, Serra-Capizzano (b13) 2018; 40 Serra-Capizzano (b32) 2002; 92 Tilli (b6) 1998; 45 Donatelli, Garoni, Manni, Serra-Capizzano, Speleers (b36) 2015; 17 Barbarino, Bianchi, Garoni (b5) 2022; 40 Ciarlet (b20) 1978 Bianchi (b11) 2021; 58 Serra-Capizzano, Tablino-Possio (b46) 2014; 51 Aricò (10.1016/j.cam.2023.115461_b26) 2004; 26 Donatelli (10.1016/j.cam.2023.115461_b27) 2021; 28 Donatelli (10.1016/j.cam.2023.115461_b28) 2012; 52 Bianchi (10.1016/j.cam.2023.115461_b11) 2021; 58 Estrada (10.1016/j.cam.2023.115461_b43) 2012; 436 Garoni (10.1016/j.cam.2023.115461_b16) 2018 Cvetkovic (10.1016/j.cam.2023.115461_b33) 1979 Garoni (10.1016/j.cam.2023.115461_b23) 2015; 36 Serra-Capizzano (10.1016/j.cam.2023.115461_b32) 2002; 92 Serra-Capizzano (10.1016/j.cam.2023.115461_b8) 2003; 366 Serra-Capizzano (10.1016/j.cam.2023.115461_b46) 2014; 51 Di Benedetto (10.1016/j.cam.2023.115461_b34) 1993; 25 Oosterlee (10.1016/j.cam.2023.115461_b31) 2001 Barbarino (10.1016/j.cam.2023.115461_b5) 2022; 40 Tilli (10.1016/j.cam.2023.115461_b6) 1998; 45 Garoni (10.1016/j.cam.2023.115461_b19) 2018 Fiorentino (10.1016/j.cam.2023.115461_b29) 1991; 28 Bianchi (10.1016/j.cam.2023.115461_b42) 2022; 61 Serra-Capizzano (10.1016/j.cam.2023.115461_b9) 2006; 419 Barbarino (10.1016/j.cam.2023.115461_b17) 2020; 53 Saad (10.1016/j.cam.2023.115461_b30) 2003 10.1016/j.cam.2023.115461_b44 Brosowski (10.1016/j.cam.2023.115461_b40) 1981; 81 Hossein Ghorban (10.1016/j.cam.2023.115461_b2) 2012; 1 Böttcher (10.1016/j.cam.2023.115461_b3) 1999 Bianchi (10.1016/j.cam.2023.115461_b12) 2018; 55 Livne (10.1016/j.cam.2023.115461_b47) 2012; 34 Garoni (10.1016/j.cam.2023.115461_b14) 2018; 7 Tilli (10.1016/j.cam.2023.115461_b10) 1998; 278 Donatelli (10.1016/j.cam.2023.115461_b36) 2015; 17 Ekström (10.1016/j.cam.2023.115461_b38) 2018; 25 Ruge (10.1016/j.cam.2023.115461_b25) 1987 Donatelli (10.1016/j.cam.2023.115461_b37) 2017; 55 Davies (10.1016/j.cam.2023.115461_b41) 1996 Keller (10.1016/j.cam.2023.115461_b24) 2021 Adriani (10.1016/j.cam.2023.115461_b1) 2020; 88 Grenander (10.1016/j.cam.2023.115461_b4) 1984 Cottrell (10.1016/j.cam.2023.115461_b21) 2009 Ciarlet (10.1016/j.cam.2023.115461_b20) 1978 Garoni (10.1016/j.cam.2023.115461_b15) 2017 Tyrtyshnikov (10.1016/j.cam.2023.115461_b7) 1998; 270 Strikwerda (10.1016/j.cam.2023.115461_b22) 1989 Barbarino (10.1016/j.cam.2023.115461_b45) 2022; 62 Donatelli (10.1016/j.cam.2023.115461_b35) 2015; 284 Lund (10.1016/j.cam.2023.115461_b39) 1992 Donatelli (10.1016/j.cam.2023.115461_b13) 2018; 40 Barbarino (10.1016/j.cam.2023.115461_b18) 2020; 53 |
| References_xml | – volume: 17 start-page: 119 year: 2015 end-page: 133 ident: b36 article-title: Two-grid optimality for Galerkin linear systems based on B-splines publication-title: Comput. Vis. Sci. – volume: 1 start-page: 35 year: 2012 end-page: 41 ident: b2 article-title: Toeplitz graph decomposition publication-title: Trans. Combinat. – volume: 366 start-page: 371 year: 2003 end-page: 402 ident: b8 article-title: Generalized locally toeplitz sequences: spectral analysis and applications to discretized partial differential equations publication-title: Linear Algebra Appl. – year: 2017 ident: b15 publication-title: The Theory of Generalized Locally Toeplitz Sequences: Theory and Applications - Vol I – year: 2018 ident: b16 publication-title: the Theory of Multilevel Generalized Locally Toeplitz Sequences: Theory and Applications - Vol II – volume: 52 start-page: 305 year: 2012 end-page: 327 ident: b28 article-title: Multigrid methods for toeplitz linear systems with different size reduction publication-title: BIT – volume: 53 start-page: 113 year: 2020 end-page: 216 ident: b18 article-title: Block generalized locally toeplitz sequences: theory and applications in the multidimensional case publication-title: Electron. Trans. Numer. Anal. – volume: 62 start-page: 681 year: 2022 end-page: 743 ident: b45 article-title: A systematic approach to reduced GLT publication-title: BIT – volume: 436 start-page: 3373 year: 2012 end-page: 3391 ident: b43 article-title: Path Laplacian matrices: introduction and application to the analysis of consensus in networks publication-title: Linear Algebra Appl. – year: 1992 ident: b39 article-title: Sinc Methods for Quadrature and Differential Equations – volume: 28 start-page: 283 year: 1991 end-page: 305 ident: b29 article-title: Multigrid methods for toeplitz matrices publication-title: Calcolo – year: 2001 ident: b31 article-title: Multigrid – volume: 419 start-page: 180 year: 2006 end-page: 233 ident: b9 article-title: The GLT class as a generalized Fourier analysis and applications publication-title: Linear Algebra Appl. – volume: 270 start-page: 15 year: 1998 end-page: 27 ident: b7 article-title: Spectra of multilevel toeplitz matrices: advanced theory via simple matrix relationships publication-title: Linear Algebra Appl. – volume: 55 start-page: 28 year: 2018 ident: b12 article-title: Spectral analysis of finite-dimensional approximations of 1d waves in non-uniform grids publication-title: Calcolo – year: 1999 ident: b3 article-title: Introduction to Large Truncated Toeplitz Matrices – volume: 25 year: 2018 ident: b38 article-title: Are the eigenvalues of the – year: 2021 ident: b24 article-title: Graphs and discrete Dirichlet spaces. Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] – volume: 88 start-page: 409 year: 2020 end-page: 454 ident: b1 article-title: Asymptotic spectra of large (grid) graphs with a uniform local structure (part I): theory publication-title: Milan J. Math. – year: 1989 ident: b22 article-title: Finite Difference Schemes and Partial Differential Equations – volume: 28 year: 2021 ident: b27 article-title: Multigrid methods for block-toeplitz linear systems: convergence analysis and applications publication-title: Numer. Linear Algebra Appl. – volume: 25 start-page: 35 year: 1993 end-page: 45 ident: b34 article-title: CG preconditioning for toeplitz matrices publication-title: Comput. Math. Appl. – year: 2003 ident: b30 article-title: Iterative Methods for Sparse Linear Systems. – volume: 92 start-page: 433 year: 2002 end-page: 465 ident: b32 article-title: Convergence analysis of two-grid methods for elliptic toeplitz and PDEs matrix-sequences publication-title: Numer. Math. – volume: 278 start-page: 91 year: 1998 end-page: 120 ident: b10 article-title: Locally toeplitz matrices: spectral theory and applications publication-title: Linear Algebra Appl. – reference: D. Bianchi, M. Donatelli, Graph approximation and generalized Tikhonov regularization for signal deblurring, in: Proceedings in IEEE International Conference on Computational Science and Its Applications, 2021, pp. 93–100. – year: 1978 ident: b20 article-title: The Finite Element Method for Elliptic Problems – volume: 81 start-page: 89 year: 1981 end-page: 92 ident: b40 article-title: An elementary proof of the stone–weierstrass theorem publication-title: Proc. Amer. Math. Soc. – volume: 7 start-page: 49 year: 2018 ident: b14 article-title: Block generalized locally toeplitz sequences: from the theory to the applications publication-title: Axioms – volume: 55 start-page: 31 year: 2017 end-page: 62 ident: b37 article-title: Symbol-based multigrid methods for Galerkin B-spline isogeometric analysis publication-title: SIAM J. Numer. Anal. – year: 2009 ident: b21 article-title: Isogeometric Analysis: Toward Integration of CAD and FEA – volume: 36 start-page: 1100 year: 2015 end-page: 1128 ident: b23 article-title: Spectral analysis and spectral symbol of publication-title: SIAM J. Matrix Anal. Appl. – volume: 284 start-page: 230 year: 2015 end-page: 264 ident: b35 article-title: Robust and optimal multi-iterative techniques for IgA Galerkin linear systems publication-title: Comput. Methods Appl. Mech. – volume: 61 start-page: 42 year: 2022 ident: b42 article-title: The generalized porous medium equation on graphs: existence and uniqueness of solutions with publication-title: Calc. Var. Partial Diff. Eq. – volume: 26 start-page: 186 year: 2004 end-page: 214 ident: b26 article-title: V-cycle optimal convergence for certain (multilevel) structured linear systems publication-title: SIAM J. Matrix Anal. Appl. – year: 1984 ident: b4 article-title: Toeplitz Forms and their Applications – year: 1987 ident: b25 article-title: Multigrid Methods – volume: 40 start-page: A4007 year: 2018 end-page: A4039 ident: b13 article-title: Spectral analysis and multigrid methods for finite volume approximations of space-fractional diffusion equations publication-title: SIAM J. Sci. Comput. – year: 1979 ident: b33 article-title: Spectra of Graphs – volume: 45 start-page: 147 year: 1998 end-page: 159 ident: b6 article-title: A note on the spectral distribution of toeplitz matrices publication-title: Linear Multilin. Algebra – year: 2018 ident: b19 article-title: The Theory of Block Generalized Locally Toeplitz Sequences – volume: 40 start-page: 155 year: 2022 end-page: -175 ident: b5 article-title: Constructive approach to the monotone rearrangement of functions publication-title: Expo. Math. – volume: 58 start-page: 47 year: 2021 ident: b11 article-title: Analysis of the spectral symbol function for discretization of a linear differential operator and analysis of the relative spectrum, with applications publication-title: Calcolo – volume: 53 start-page: 28 year: 2020 end-page: 112 ident: b17 article-title: Block generalized locally toeplitz sequences: theory and applications in the unidimensional case publication-title: Electron. Trans. Numer. Anal. – volume: 51 start-page: 261 year: 2014 end-page: 285 ident: b46 article-title: Two-grid methods for hermitian positive definite linear systems connected with an order relation publication-title: Calcolo – year: 1996 ident: b41 article-title: Spectral Theory and Differential Operators – volume: 34 start-page: 499 year: 2012 end-page: 522 ident: b47 article-title: Lean algebraic multigrid (LAMG): fast graph Laplacian linear solver publication-title: SIAM J. Sci. Comput. – volume: 51 start-page: 261 issue: 2 year: 2014 ident: 10.1016/j.cam.2023.115461_b46 article-title: Two-grid methods for hermitian positive definite linear systems connected with an order relation publication-title: Calcolo doi: 10.1007/s10092-013-0081-9 – year: 1999 ident: 10.1016/j.cam.2023.115461_b3 – volume: 40 start-page: 155 issue: 1 year: 2022 ident: 10.1016/j.cam.2023.115461_b5 article-title: Constructive approach to the monotone rearrangement of functions publication-title: Expo. Math. doi: 10.1016/j.exmath.2021.10.004 – volume: 52 start-page: 305 issue: 2 year: 2012 ident: 10.1016/j.cam.2023.115461_b28 article-title: Multigrid methods for toeplitz linear systems with different size reduction publication-title: BIT doi: 10.1007/s10543-011-0356-y – volume: 7 start-page: 49 issue: 3 year: 2018 ident: 10.1016/j.cam.2023.115461_b14 article-title: Block generalized locally toeplitz sequences: from the theory to the applications publication-title: Axioms doi: 10.3390/axioms7030049 – year: 1987 ident: 10.1016/j.cam.2023.115461_b25 – volume: 53 start-page: 28 year: 2020 ident: 10.1016/j.cam.2023.115461_b17 article-title: Block generalized locally toeplitz sequences: theory and applications in the unidimensional case publication-title: Electron. Trans. Numer. Anal. doi: 10.1553/etna_vol53s28 – year: 1978 ident: 10.1016/j.cam.2023.115461_b20 – volume: 92 start-page: 433 issue: 3 year: 2002 ident: 10.1016/j.cam.2023.115461_b32 article-title: Convergence analysis of two-grid methods for elliptic toeplitz and PDEs matrix-sequences publication-title: Numer. Math. doi: 10.1007/s002110100331 – volume: 25 issue: 5 year: 2018 ident: 10.1016/j.cam.2023.115461_b38 article-title: Are the eigenvalues of the B-spline isogeometric analysis approximation of −Δu=λu known in almost closed form? – volume: 81 start-page: 89 issue: 1 year: 1981 ident: 10.1016/j.cam.2023.115461_b40 article-title: An elementary proof of the stone–weierstrass theorem publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-1981-0589143-8 – volume: 28 start-page: 283 year: 1991 ident: 10.1016/j.cam.2023.115461_b29 article-title: Multigrid methods for toeplitz matrices publication-title: Calcolo doi: 10.1007/BF02575816 – volume: 436 start-page: 3373 year: 2012 ident: 10.1016/j.cam.2023.115461_b43 article-title: Path Laplacian matrices: introduction and application to the analysis of consensus in networks publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2011.11.032 – volume: 88 start-page: 409 year: 2020 ident: 10.1016/j.cam.2023.115461_b1 article-title: Asymptotic spectra of large (grid) graphs with a uniform local structure (part I): theory publication-title: Milan J. Math. doi: 10.1007/s00032-020-00319-2 – volume: 419 start-page: 180 year: 2006 ident: 10.1016/j.cam.2023.115461_b9 article-title: The GLT class as a generalized Fourier analysis and applications publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2006.04.012 – volume: 270 start-page: 15 year: 1998 ident: 10.1016/j.cam.2023.115461_b7 article-title: Spectra of multilevel toeplitz matrices: advanced theory via simple matrix relationships publication-title: Linear Algebra Appl. doi: 10.1016/S0024-3795(97)80001-8 – year: 2009 ident: 10.1016/j.cam.2023.115461_b21 – volume: 58 start-page: 47 year: 2021 ident: 10.1016/j.cam.2023.115461_b11 article-title: Analysis of the spectral symbol function for discretization of a linear differential operator and analysis of the relative spectrum, with applications publication-title: Calcolo doi: 10.1007/s10092-021-00426-5 – volume: 62 start-page: 681 issue: 3 year: 2022 ident: 10.1016/j.cam.2023.115461_b45 article-title: A systematic approach to reduced GLT publication-title: BIT doi: 10.1007/s10543-021-00896-7 – volume: 26 start-page: 186 year: 2004 ident: 10.1016/j.cam.2023.115461_b26 article-title: V-cycle optimal convergence for certain (multilevel) structured linear systems publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479803421987 – year: 2018 ident: 10.1016/j.cam.2023.115461_b16 – volume: 61 start-page: 42 issue: 5 year: 2022 ident: 10.1016/j.cam.2023.115461_b42 article-title: The generalized porous medium equation on graphs: existence and uniqueness of solutions with ℓ1 data publication-title: Calc. Var. Partial Diff. Eq. doi: 10.1007/s00526-022-02249-w – volume: 28 issue: 4 year: 2021 ident: 10.1016/j.cam.2023.115461_b27 article-title: Multigrid methods for block-toeplitz linear systems: convergence analysis and applications publication-title: Numer. Linear Algebra Appl. doi: 10.1002/nla.2356 – volume: 45 start-page: 147 year: 1998 ident: 10.1016/j.cam.2023.115461_b6 article-title: A note on the spectral distribution of toeplitz matrices publication-title: Linear Multilin. Algebra doi: 10.1080/03081089808818584 – year: 2018 ident: 10.1016/j.cam.2023.115461_b19 – year: 1989 ident: 10.1016/j.cam.2023.115461_b22 – year: 1979 ident: 10.1016/j.cam.2023.115461_b33 – year: 1996 ident: 10.1016/j.cam.2023.115461_b41 – year: 2021 ident: 10.1016/j.cam.2023.115461_b24 – volume: 55 start-page: 28 year: 2018 ident: 10.1016/j.cam.2023.115461_b12 article-title: Spectral analysis of finite-dimensional approximations of 1d waves in non-uniform grids publication-title: Calcolo doi: 10.1007/s10092-018-0288-x – volume: 366 start-page: 371 year: 2003 ident: 10.1016/j.cam.2023.115461_b8 article-title: Generalized locally toeplitz sequences: spectral analysis and applications to discretized partial differential equations publication-title: Linear Algebra Appl. doi: 10.1016/S0024-3795(02)00504-9 – volume: 40 start-page: A4007 issue: 6 year: 2018 ident: 10.1016/j.cam.2023.115461_b13 article-title: Spectral analysis and multigrid methods for finite volume approximations of space-fractional diffusion equations publication-title: SIAM J. Sci. Comput. doi: 10.1137/17M115164X – volume: 53 start-page: 113 year: 2020 ident: 10.1016/j.cam.2023.115461_b18 article-title: Block generalized locally toeplitz sequences: theory and applications in the multidimensional case publication-title: Electron. Trans. Numer. Anal. doi: 10.1553/etna_vol53s113 – volume: 1 start-page: 35 issue: 4 year: 2012 ident: 10.1016/j.cam.2023.115461_b2 article-title: Toeplitz graph decomposition publication-title: Trans. Combinat. – volume: 25 start-page: 35 issue: 6 year: 1993 ident: 10.1016/j.cam.2023.115461_b34 article-title: CG preconditioning for toeplitz matrices publication-title: Comput. Math. Appl. doi: 10.1016/0898-1221(93)90297-9 – volume: 17 start-page: 119 year: 2015 ident: 10.1016/j.cam.2023.115461_b36 article-title: Two-grid optimality for Galerkin linear systems based on B-splines publication-title: Comput. Vis. Sci. doi: 10.1007/s00791-015-0253-z – volume: 278 start-page: 91 year: 1998 ident: 10.1016/j.cam.2023.115461_b10 article-title: Locally toeplitz matrices: spectral theory and applications publication-title: Linear Algebra Appl. doi: 10.1016/S0024-3795(97)10079-9 – volume: 55 start-page: 31 issue: 1 year: 2017 ident: 10.1016/j.cam.2023.115461_b37 article-title: Symbol-based multigrid methods for Galerkin B-spline isogeometric analysis publication-title: SIAM J. Numer. Anal. doi: 10.1137/140988590 – year: 2001 ident: 10.1016/j.cam.2023.115461_b31 – year: 1984 ident: 10.1016/j.cam.2023.115461_b4 – volume: 34 start-page: 499 issue: 4 year: 2012 ident: 10.1016/j.cam.2023.115461_b47 article-title: Lean algebraic multigrid (LAMG): fast graph Laplacian linear solver publication-title: SIAM J. Sci. Comput. doi: 10.1137/110843563 – volume: 284 start-page: 230 year: 2015 ident: 10.1016/j.cam.2023.115461_b35 article-title: Robust and optimal multi-iterative techniques for IgA Galerkin linear systems publication-title: Comput. Methods Appl. Mech. doi: 10.1016/j.cma.2014.06.001 – ident: 10.1016/j.cam.2023.115461_b44 doi: 10.1109/ICCSA54496.2021.00023 – year: 2017 ident: 10.1016/j.cam.2023.115461_b15 – volume: 36 start-page: 1100 issue: 3 year: 2015 ident: 10.1016/j.cam.2023.115461_b23 article-title: Spectral analysis and spectral symbol of d-variate Qp Lagrangian FEM stiffness matrices publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/140976480 – year: 1992 ident: 10.1016/j.cam.2023.115461_b39 – year: 2003 ident: 10.1016/j.cam.2023.115461_b30 |
| SSID | ssj0006914 |
| Score | 2.4086897 |
| Snippet | In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain Ω⊂Rd, d≥1. When... In the current work we are concerned with sequences of graphs having a grid geometry, with a uniform local structure in a bounded domain Ω ⊂ R d , d ≥ 1. When... |
| SourceID | swepub crossref elsevier |
| SourceType | Open Access Repository Enrichment Source Index Database Publisher |
| StartPage | 115461 |
| SubjectTerms | Asymptotic spectra Beräkningsvetenskap med inriktning mot numerisk analys Graph Laplacian Graphs Multigrid methods PDE discretizations Preconditioning Scientific Computing with specialization in Numerical Analysis |
| Title | Asymptotic spectra of large (grid) graphs with a uniform local structure, Part II: Numerical applications |
| URI | https://dx.doi.org/10.1016/j.cam.2023.115461 https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-509946 |
| Volume | 437 |
| WOSCitedRecordID | wos001066522800001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1879-1778 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0006914 issn: 1879-1778 databaseCode: AIEXJ dateStart: 20211209 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1db9MwFLXKxgM8THyKMUB-AAkImfLhxA5v1dhEEVRIG6hvkePEI1ObVl07jf0mfiT32nFabdoESLxEkVPHke-pfXJz77mEvBRxBaS_1H4iZOWzuAr9IuShzxljQalx0zRVSz7z4VCMRtnXXu-Xy4U5G_OmEefn2ey_mhrawNiYOvsX5u5uCg1wDkaHI5gdjn9k-P7pz8lsMUUhVpNGOZdICMcY8Y108niOT5R5Rqna5bZ5ywYztCae2do8Kyq7bBPAYAxvMEDXwXBpv--MvfXv3tfwW2XqRThfo9GEbRnvpJOK7Qh9v4SZMdWlbIjlyk2ATpcfdRd-3-HwoMIC9bV9wum463CI7f6enNUXF9LUFcdINg2n6w6OiLmYaOd1u5J5Y7O9OPexTojdx-ziLXjmh9yWBHKrO7OaMld2Cuu0ONlVEvUIongXdYmsLvwlAe5DHAuHilCdDBatW2Qz4kkGa-hmf7A_-tTt_GlmteTds7mv6Cae8NJA1_KgdcFaQ3KO7pGt1nq0b1F1n_Sq5gG5-2Vlr4ekXuGLtviiU00NvuhrRNcbarFFEVtU0hZb1GCLdth6RxFZdDB4Tztc0XVcPSLfDvaP9j76bb0OX8UxW-CLmkgDnZSCMRmqpFBJqnSoSwkrQgYvspkqVFSGgRJcJAWLFJDbVDCRMCnLIowfk41m2lRPCOXAYnUacKULuMgTqUMlNA9VJQJRRNE2Cdzs5aoVs8eaKuPcRS2e5DDhOU54bid8m7ztusyskstNP2bOJHlLRS3FzAE_N3V7Zc3XjYDq7R_q7_18Oj_Ol8sc-HnG0qf_dvsdcmf1B3lGNsBg1XNyW50t6tP5ixaNvwH_SbsQ |
| linkProvider | Elsevier |
| 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=Asymptotic+spectra+of+large+%28grid%29+graphs+with+a+uniform+local+structure%2C+Part+II%3A+Numerical+applications&rft.jtitle=Journal+of+computational+and+applied+mathematics&rft.au=Adriani%2C+Andrea&rft.au=Bianchi%2C+Davide&rft.au=Ferrari%2C+Paola&rft.au=Serra-Capizzano%2C+Stefano&rft.date=2024-02-01&rft.pub=Elsevier+B.V&rft.issn=0377-0427&rft.eissn=1879-1778&rft.volume=437&rft_id=info:doi/10.1016%2Fj.cam.2023.115461&rft.externalDocID=S0377042723004053 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-0427&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-0427&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-0427&client=summon |