DOI: 10.1016/s0167-8191(00)00100-9. Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems

Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems

10.1016/s0167-8191(00)00100-9

Crossref journal-article

Elsevier BV

Parallel Computing (78)

Bibliography

Censor, Y., Gordon, D., & Gordon, R. (2001). Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems. Parallel Computing, 27(6), 777â808.

Authors 3

Yair Censor (first)
Dan Gordon (additional)
Rachel Gordon (additional)

References 35 Referenced 159

10.1016/0024-3795(89)90375-3 / Linear Algebra Appl. / Block-iterative projection methods for parallel computation of solutions to convex feasibility problems by Aharoni (1989)
10.1137/0913003 / SIAM J. Sci. Stat. Comput. / A block projection method for sparse matrices by Arioli (1992)
10.1137/S0036144593251710 / SIAM Rev. / On projection algorithms for solving convex feasibility problems by Bauschke (1996)
10.1109/78.286957 / IEEE Trans. Signal Process. / Signal processing applications of oblique projection operators by Behrens (1994)
{'key': '10.1016/S0167-8191(00)00100-9_BIB5', 'series-title': 'Generalized Inverses: Theory and Applications', 'author': 'Ben-Israel', 'year': '1974'} / Generalized Inverses: Theory and Applications by Ben-Israel (1974)
{'key': '10.1016/S0167-8191(00)00100-9_BIB6', 'series-title': 'Parallel and Distributed Computation: Numerical Methods', 'author': 'Bertsekas', 'year': '1989'} / Parallel and Distributed Computation: Numerical Methods by Bertsekas (1989)
{'key': '10.1016/S0167-8191(00)00100-9_BIB7', 'series-title': 'Numerical Methods for Least squares Problems', 'author': 'Björck', 'year': '1996'} / Numerical Methods for Least squares Problems by Björck (1996)
10.1016/0041-5553(67)90040-7 / USSR Comput. Math. Math. Phys. / The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming by Bregman (1967)
J.A. Browne, G.T. Herman, D. Odhner, SNARK93: a programming system for image reconstruction from projections, Technical Report No. MIPG198, The Medical Image Processing Group (MIPG). Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA, August 1993
C. Byrne, Y. Censor, Proximity function minimization for separable, jointly convex Bregman distances, with applications, Technical Report, February 1998
C. Byrne, Y. Censor, Proximity function minimization using multiple Bregman projections, with applications to entropy optimization and Kullback–Leibler distance minimization, Technical Report, June 1999, revised: May 2000, Ann. Oper. Res. (to appear)
10.1109/PROC.1983.12598 / Proc. IEEE / Finite series-expansion reconstruction methods by Censor (1983)
10.1007/BF01396307 / Numer. Math. / Strong underrelaxation in Kaczmarz's method for inconsistent systems by Censor (1983)
{'key': '10.1016/S0167-8191(00)00100-9_BIB14', 'series-title': 'Parallel Optimization: Theory, Algorithms and Applications', 'author': 'Censor', 'year': '1997'} / Parallel Optimization: Theory, Algorithms and Applications by Censor (1997)
{'key': '10.1016/S0167-8191(00)00100-9_BIB15', 'first-page': '326', 'article-title': 'Calcolo approssimato per soluzioni dei sistemi di equazioni lineari', 'volume': '1', 'author': 'Cimmino', 'year': '1938', 'journal-title': 'La Ricerca Scientifica XVI, Series II, Anno IX'} / La Ricerca Scientifica XVI, Series II, Anno IX / Calcolo approssimato per soluzioni dei sistemi di equazioni lineari by Cimmino (1938)
10.1109/78.330356 / IEEE Trans. Signal Process. / Inconsistent signal feasibility problems: least-squares solutions in a product space by Combettes (1994)
10.1007/BF02144106 / Numer. Algo. / A parallel projection method for overdetermined nonlinear systems of equations by Diniz-Ehrhardt (1993)
10.1016/0024-3795(81)90139-7 / Linear Algebra Appl. / Iterative algorithms for large partitioned linear systems, with applications to image reconstruction by Eggermont (1981)
10.1007/BF01396365 / Numer. Math. / Block-iterative methods for consistent and inconsistent linear equations by Elfving (1980)
{'key': '10.1016/S0167-8191(00)00100-9_BIB20', 'series-title': 'Linear Numerical Analysis', 'author': 'Gastinel', 'year': '1970'} / Linear Numerical Analysis by Gastinel (1970)
{'key': '10.1016/S0167-8191(00)00100-9_BIB21', 'series-title': 'Image Reconstruction From Projections: The Fundamentals of Computerized Tomography', 'author': 'Herman', 'year': '1980'} / Image Reconstruction From Projections: The Fundamentals of Computerized Tomography by Herman (1980)
10.1109/42.241889 / IEEE Trans. Med. Imag. / Algebraic reconstruction techniques can be made computationally efficient by Herman (1993)
10.1007/BF01389537 / Numer. Math. / Convergence results for an accelerated nonlinear Cimmino algorithm by Iusem (1986)
{'key': '10.1016/S0167-8191(00)00100-9_BIB24', 'first-page': '355', 'article-title': 'Angenäherte auflösung von systemen linearer gleichungen', 'volume': 'A35', 'author': 'Kaczmarz', 'year': '1937', 'journal-title': "Bulletin de l' Académie Polonaise des Sciences et Lettres"} / Bulletin de l' Académie Polonaise des Sciences et Lettres / Angenäherte auflösung von systemen linearer gleichungen by Kaczmarz (1937)
10.1007/BF02551360 / Math. Control Signals Syst. / Oblique projections: formulas, algorithms, and error bounds by Kayalar (1989)
10.1137/S1052623494278347 / SIAM J. Optim. / A projection-based algorithm for consistent and inconsistent constraints by Kotzer (1997)
{'key': '10.1016/S0167-8191(00)00100-9_BIB27', 'series-title': 'Introductory Functional Analysis with Applications', 'author': 'Kreyszig', 'year': '1978'} / Introductory Functional Analysis with Applications by Kreyszig (1978)
10.1090/S0002-9947-1939-1501988-6 / Trans. Am. Math. Soc. / On a calculus of operators in reflexive vector spaces by Lorch (1939)
10.1016/0377-0427(86)90222-0 / J. Comput. Appl. Math. / Parallel and sequential Kaczmarz methods for solving underdetermined nonlinear equations by Martinez (1986)
{'key': '10.1016/S0167-8191(00)00100-9_BIB30', 'first-page': '138', 'article-title': 'On complementary manifolds and projections in Lp and lp', 'volume': '41', 'author': 'Murray', 'year': '1937', 'journal-title': 'Trans. Am. Math. Soc.'} / Trans. Am. Math. Soc. / On complementary manifolds and projections in Lp and lp by Murray (1937)
10.1109/42.192683 / IEEE Trans. Med. Imag. / Acceleration of Landweber-type algorithms by suppression of projection on the maximum singular vector by Pan (1992)
10.1109/42.232256 / IEEE Trans. Med. Imag. / Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix by Pan (1993)
10.1007/BF02612715 / Math. Prog. / Decomposition through formalization in a product space by Pierra (1984)
10.1007/BF01436376 / Numer. Math. / Projection method for solving a singular system of linear equations and its applications by Tanabe (1971)
10.1109/TASSP.1985.1164752 / IEEE Trans. Acoust. Speech Signal Process. / The Landweber iteration and projection onto convex sets by Trussell (1985)

Dates

Type	When
Created	23 years, 1 month ago (July 25, 2002, 12:51 p.m.)
Deposited	6 years, 4 months ago (April 20, 2019, 5:21 p.m.)
Indexed	1 month ago (July 27, 2025, 3:44 a.m.)
Issued	24 years, 3 months ago (May 1, 2001)
Published	24 years, 3 months ago (May 1, 2001)
Published Print	24 years, 3 months ago (May 1, 2001)

Funders 0

None

BibTeX

@article{Censor_2001, title={Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems}, volume={27}, ISSN={0167-8191}, url={http://dx.doi.org/10.1016/s0167-8191(00)00100-9}, DOI={10.1016/s0167-8191(00)00100-9}, number={6}, journal={Parallel Computing}, publisher={Elsevier BV}, author={Censor, Yair and Gordon, Dan and Gordon, Rachel}, year={2001}, month=may, pages={777–808} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        7,
        27
      ]
    ],
    "date-time": "2025-07-27T07:44:19Z",
    "timestamp": 1753602259236
  },
  "reference-count": 35,
  "publisher": "Elsevier BV",
  "issue": "6",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2001,
            5,
            1
          ]
        ],
        "date-time": "2001-05-01T00:00:00Z",
        "timestamp": 988675200000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://www.elsevier.com/tdm/userlicense/1.0/"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2001,
        5
      ]
    ]
  },
  "DOI": "10.1016/s0167-8191(00)00100-9",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        25
      ]
    ],
    "date-time": "2002-07-25T16:51:54Z",
    "timestamp": 1027615914000
  },
  "page": "777-808",
  "source": "Crossref",
  "is-referenced-by-count": 159,
  "title": "Component averaging: An efficient iterative parallel algorithm for large and sparse unstructured problems",
  "prefix": "10.1016",
  "volume": "27",
  "author": [
    {
      "given": "Yair",
      "family": "Censor",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "Dan",
      "family": "Gordon",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Rachel",
      "family": "Gordon",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "78",
  "reference": [
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB1",
      "doi-asserted-by": "crossref",
      "first-page": "165",
      "DOI": "10.1016/0024-3795(89)90375-3",
      "article-title": "Block-iterative projection methods for parallel computation of solutions to convex feasibility problems",
      "volume": "120",
      "author": "Aharoni",
      "year": "1989",
      "journal-title": "Linear Algebra Appl."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB2",
      "doi-asserted-by": "crossref",
      "first-page": "47",
      "DOI": "10.1137/0913003",
      "article-title": "A block projection method for sparse matrices",
      "volume": "13",
      "author": "Arioli",
      "year": "1992",
      "journal-title": "SIAM J. Sci. Stat. Comput."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB3",
      "doi-asserted-by": "crossref",
      "first-page": "367",
      "DOI": "10.1137/S0036144593251710",
      "article-title": "On projection algorithms for solving convex feasibility problems",
      "volume": "38",
      "author": "Bauschke",
      "year": "1996",
      "journal-title": "SIAM Rev."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB4",
      "doi-asserted-by": "crossref",
      "first-page": "1413",
      "DOI": "10.1109/78.286957",
      "article-title": "Signal processing applications of oblique projection operators",
      "volume": "SP-42",
      "author": "Behrens",
      "year": "1994",
      "journal-title": "IEEE Trans. Signal Process."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB5",
      "series-title": "Generalized Inverses: Theory and Applications",
      "author": "Ben-Israel",
      "year": "1974"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB6",
      "series-title": "Parallel and Distributed Computation: Numerical Methods",
      "author": "Bertsekas",
      "year": "1989"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB7",
      "series-title": "Numerical Methods for Least squares Problems",
      "author": "Bj\u00f6rck",
      "year": "1996"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB8",
      "doi-asserted-by": "crossref",
      "first-page": "200",
      "DOI": "10.1016/0041-5553(67)90040-7",
      "article-title": "The relaxation method for finding the common point of convex sets and its application to the solution of problems in convex programming",
      "volume": "7",
      "author": "Bregman",
      "year": "1967",
      "journal-title": "USSR Comput. Math. Math. Phys."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB9",
      "unstructured": "J.A. Browne, G.T. Herman, D. Odhner, SNARK93: a programming system for image reconstruction from projections, Technical Report No. MIPG198, The Medical Image Processing Group (MIPG). Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA, August 1993"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB10",
      "unstructured": "C. Byrne, Y. Censor, Proximity function minimization for separable, jointly convex Bregman distances, with applications, Technical Report, February 1998"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB11",
      "unstructured": "C. Byrne, Y. Censor, Proximity function minimization using multiple Bregman projections, with applications to entropy optimization and Kullback\u2013Leibler distance minimization, Technical Report, June 1999, revised: May 2000, Ann. Oper. Res. (to appear)"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB12",
      "doi-asserted-by": "crossref",
      "first-page": "409",
      "DOI": "10.1109/PROC.1983.12598",
      "article-title": "Finite series-expansion reconstruction methods",
      "volume": "71",
      "author": "Censor",
      "year": "1983",
      "journal-title": "Proc. IEEE"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB13",
      "doi-asserted-by": "crossref",
      "first-page": "83",
      "DOI": "10.1007/BF01396307",
      "article-title": "Strong underrelaxation in Kaczmarz's method for inconsistent systems",
      "volume": "41",
      "author": "Censor",
      "year": "1983",
      "journal-title": "Numer. Math."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB14",
      "series-title": "Parallel Optimization: Theory, Algorithms and Applications",
      "author": "Censor",
      "year": "1997"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB15",
      "first-page": "326",
      "article-title": "Calcolo approssimato per soluzioni dei sistemi di equazioni lineari",
      "volume": "1",
      "author": "Cimmino",
      "year": "1938",
      "journal-title": "La Ricerca Scientifica XVI, Series II, Anno IX"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB16",
      "doi-asserted-by": "crossref",
      "first-page": "2955",
      "DOI": "10.1109/78.330356",
      "article-title": "Inconsistent signal feasibility problems: least-squares solutions in a product space",
      "volume": "SP-42",
      "author": "Combettes",
      "year": "1994",
      "journal-title": "IEEE Trans. Signal Process."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB17",
      "doi-asserted-by": "crossref",
      "first-page": "241",
      "DOI": "10.1007/BF02144106",
      "article-title": "A parallel projection method for overdetermined nonlinear systems of equations",
      "volume": "4",
      "author": "Diniz-Ehrhardt",
      "year": "1993",
      "journal-title": "Numer. Algo."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB18",
      "doi-asserted-by": "crossref",
      "first-page": "37",
      "DOI": "10.1016/0024-3795(81)90139-7",
      "article-title": "Iterative algorithms for large partitioned linear systems, with applications to image reconstruction",
      "volume": "40",
      "author": "Eggermont",
      "year": "1981",
      "journal-title": "Linear Algebra Appl."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB19",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1007/BF01396365",
      "article-title": "Block-iterative methods for consistent and inconsistent linear equations",
      "volume": "35",
      "author": "Elfving",
      "year": "1980",
      "journal-title": "Numer. Math."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB20",
      "series-title": "Linear Numerical Analysis",
      "author": "Gastinel",
      "year": "1970"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB21",
      "series-title": "Image Reconstruction From Projections: The Fundamentals of Computerized Tomography",
      "author": "Herman",
      "year": "1980"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB22",
      "doi-asserted-by": "crossref",
      "first-page": "600",
      "DOI": "10.1109/42.241889",
      "article-title": "Algebraic reconstruction techniques can be made computationally efficient",
      "volume": "MI-12",
      "author": "Herman",
      "year": "1993",
      "journal-title": "IEEE Trans. Med. Imag."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB23",
      "doi-asserted-by": "crossref",
      "first-page": "367",
      "DOI": "10.1007/BF01389537",
      "article-title": "Convergence results for an accelerated nonlinear Cimmino algorithm",
      "volume": "49",
      "author": "Iusem",
      "year": "1986",
      "journal-title": "Numer. Math."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB24",
      "first-page": "355",
      "article-title": "Angen\u00e4herte aufl\u00f6sung von systemen linearer gleichungen",
      "volume": "A35",
      "author": "Kaczmarz",
      "year": "1937",
      "journal-title": "Bulletin de l' Acad\u00e9mie Polonaise des Sciences et Lettres"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB25",
      "doi-asserted-by": "crossref",
      "first-page": "33",
      "DOI": "10.1007/BF02551360",
      "article-title": "Oblique projections: formulas, algorithms, and error bounds",
      "volume": "2",
      "author": "Kayalar",
      "year": "1989",
      "journal-title": "Math. Control Signals Syst."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB26",
      "doi-asserted-by": "crossref",
      "first-page": "527",
      "DOI": "10.1137/S1052623494278347",
      "article-title": "A projection-based algorithm for consistent and inconsistent constraints",
      "volume": "7",
      "author": "Kotzer",
      "year": "1997",
      "journal-title": "SIAM J. Optim."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB27",
      "series-title": "Introductory Functional Analysis with Applications",
      "author": "Kreyszig",
      "year": "1978"
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB28",
      "doi-asserted-by": "crossref",
      "first-page": "217",
      "DOI": "10.1090/S0002-9947-1939-1501988-6",
      "article-title": "On a calculus of operators in reflexive vector spaces",
      "volume": "45",
      "author": "Lorch",
      "year": "1939",
      "journal-title": "Trans. Am. Math. Soc."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB29",
      "doi-asserted-by": "crossref",
      "first-page": "311",
      "DOI": "10.1016/0377-0427(86)90222-0",
      "article-title": "Parallel and sequential Kaczmarz methods for solving underdetermined nonlinear equations",
      "volume": "15",
      "author": "Martinez",
      "year": "1986",
      "journal-title": "J. Comput. Appl. Math."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB30",
      "first-page": "138",
      "article-title": "On complementary manifolds and projections in Lp and lp",
      "volume": "41",
      "author": "Murray",
      "year": "1937",
      "journal-title": "Trans. Am. Math. Soc."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB31",
      "doi-asserted-by": "crossref",
      "first-page": "479",
      "DOI": "10.1109/42.192683",
      "article-title": "Acceleration of Landweber-type algorithms by suppression of projection on the maximum singular vector",
      "volume": "MI-11",
      "author": "Pan",
      "year": "1992",
      "journal-title": "IEEE Trans. Med. Imag."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB32",
      "doi-asserted-by": "crossref",
      "first-page": "278",
      "DOI": "10.1109/42.232256",
      "article-title": "Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix",
      "volume": "MI-12",
      "author": "Pan",
      "year": "1993",
      "journal-title": "IEEE Trans. Med. Imag."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB33",
      "doi-asserted-by": "crossref",
      "first-page": "96",
      "DOI": "10.1007/BF02612715",
      "article-title": "Decomposition through formalization in a product space",
      "volume": "28",
      "author": "Pierra",
      "year": "1984",
      "journal-title": "Math. Prog."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB34",
      "doi-asserted-by": "crossref",
      "first-page": "203",
      "DOI": "10.1007/BF01436376",
      "article-title": "Projection method for solving a singular system of linear equations and its applications",
      "volume": "17",
      "author": "Tanabe",
      "year": "1971",
      "journal-title": "Numer. Math."
    },
    {
      "key": "10.1016/S0167-8191(00)00100-9_BIB35",
      "doi-asserted-by": "crossref",
      "first-page": "1632",
      "DOI": "10.1109/TASSP.1985.1164752",
      "article-title": "The Landweber iteration and projection onto convex sets",
      "volume": "ASSP-33",
      "author": "Trussell",
      "year": "1985",
      "journal-title": "IEEE Trans. Acoust. Speech Signal Process."
    }
  ],
  "container-title": "Parallel Computing",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0167819100001009?httpAccept=text/xml",
      "content-type": "text/xml",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0167819100001009?httpAccept=text/plain",
      "content-type": "text/plain",
      "content-version": "vor",
      "intended-application": "text-mining"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2019,
        4,
        20
      ]
    ],
    "date-time": "2019-04-20T21:21:07Z",
    "timestamp": 1555795267000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://linkinghub.elsevier.com/retrieve/pii/S0167819100001009"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2001,
        5
      ]
    ]
  },
  "references-count": 35,
  "journal-issue": {
    "issue": "6",
    "published-print": {
      "date-parts": [
        [
          2001,
          5
        ]
      ]
    }
  },
  "alternative-id": [
    "S0167819100001009"
  ],
  "URL": "http://dx.doi.org/10.1016/S0167-8191(00)00100-9",
  "relation": {},
  "ISSN": [
    "0167-8191"
  ],
  "subject": [],
  "container-title-short": "Parallel Computing",
  "published": {
    "date-parts": [
      [
        2001,
        5
      ]
    ]
  }
}