DOI: 10.1007/bf01934268. Least-squares fitting of circles and ellipses

Least-squares fitting of circles and ellipses

10.1007/bf01934268

Crossref journal-article

Springer Science and Business Media LLC

BIT (297)

Bibliography

Gander, W., Golub, G. H., & Strebel, R. (1994). Least-squares fitting of circles and ellipses. BIT, 34(4), 558â578.

Authors 3

Walter Gander (first)
Gene H. Golub (additional)
Rolf Strebel (additional)

References 17 Referenced 652

V. Pratt,Direct Least Squares Fitting of Algebraic Surfaces, ACM J. Computer Graphics, Volume 21, Number 4, July 1987. (10.1145/37402.37420)
M. G. Cox, A. B. Forbes,Strategies for Testing Assessment Software, Technical Report NPL DITC 211/92, National Physical Laboratory, Teddington, UK., 1992. / Strategies for Testing Assessment Software / Technical Report NPL DITC 211/92 by M. G. Cox (1992)
G. H. Golub, Ch. Van Loan,Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, MD., 1989. / Matrix Computations by G. H. Golub (1989)
D. Sourlier, A. Bucher,Normgerechter Best-fit-Algorithms für Freiform-Flächen oder andere nicht-reguläre Ausgleichs-Flächen in Parameter-Form, Technisches Messen 59 (1992), pp. 293–302. (10.1524/teme.1992.59.78.293) / Technisches Messen by D. Sourlier (1992)
H. Späth,Orthogonal least squares fitting with linear manifolds, Numer. Math., 48 (1986), pp. 441–445. (10.1007/BF01389650) / Numer. Math. by H. Späth (1986)
L. B. Smith,The use of man-machine interaction in data fitting problems, TR CS 131, Computer Science Department, Stanford University, Stanford, CA, Ph.D. thesis, March 1969. (10.2172/4779098) / The use of man-machine interaction in data fitting problems by L. B. Smith (1969)
Y. V. Linnik,Method of least squares and principles of the theory of observations, Pergamon Press, New York, 1961. / Method of least squares and principles of the theory of observations by Y. V. Linnik (1961)
C. L. Lawson,Contributions to the theory of linear least maximum approximation, UCLA, Los Angeles, Ph.D. thesis, 1961. / Contributions to the theory of linear least maximum approximation by C. L. Lawson (1961)
Fred L. Bookstein,Fitting conic sections to scattered data, Computer Graphics and Image Processing 9, (1979), pp. 56–71. (10.1016/0146-664X(79)90082-0) / Computer Graphics and Image Processing by Fred L. Bookstein (1979)
G. H. golub, V. Pereyra,The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate, SIAM J. Numer. Anal. 10, No. 2, (1973), pp. 413–432. (10.1137/0710036) / SIAM J. Numer. Anal. by G. H. golub (1973)
M. Heidari, P. C. Heigold,Determination of Hydraulic Conductivity Tensor Using a Nonlinear Least Squares Estimator, Water Resources Bulletin, June 1993, pp. 415–424. (10.1111/j.1752-1688.1993.tb03219.x)
W. Gander, U. von Matt,Some Least Squares Problems, in Solving Problems in Scientific Computing Using Maple and Matlab, W. Gander and J. Hřebíček, eds., Springer-Verlag, 1993, pp. 251–266. (10.1007/978-3-642-97533-2)
Paul T. Boggs, Richard H. Byrd and Robert B. Schnabel,A stable and efficient algorithm for nonlinear orthogonal distance regression, SIAM J. Sci. and Statist. Comput. 8 (1987), pp. 1052–1078. (10.1137/0908085) / SIAM J. Sci. and Statist. Comput. by Paul T. Boggs (1987)
Paul T. Boggs, Richard H. Byrd, Janet E. Rogers and Robert B. Schnabel,User's Reference Guide for ODRPACK Verion 2.01—Software for Weighted Orthogonal Distance Regression, National Institute of Standards and Technology, Gaithersburg, June 1992. (10.6028/NIST.IR.4834) / User's Reference Guide for ODRPACK Verion 2.01—Software for Weighted Orthogonal Distance Regression by Paul T. Boggs (1992)
P. E. Gill, W. Murray and M. H. Wright,Practical Optimization, Academic Press, New York, 1981. / Practical Optimization by P. E. Gill (1981)
Gene H. Golub, Alan Hoffman, G. W. Stewart,A generalization of the Eckart-Young-Mirsky Matrix Approximation Theorem, Linear Algebra Appl., 88/89 (1987), pp. 317–327. (10.1016/0024-3795(87)90114-5) / Linear Algebra Appl. by Gene H. Golub (1987)
Walter Gander, Gene H. Golub, and Rolf Strebel,Fitting of circles and ellipses—least squares solution, Technical Report 217, Insitiut für Wisenschaftliches Rechnen, ETH Zürich, June 1994. Available via anonymous ftp from fip.inf.ethz.ch as doc/tech-reports/1994/217.ps.

Dates

Type	When
Created	20 years ago (July 30, 2005, 9:06 p.m.)
Deposited	5 years, 4 months ago (April 8, 2020, 9:10 a.m.)
Indexed	20 hours, 3 minutes ago (Aug. 20, 2025, 8:47 a.m.)
Issued	30 years, 8 months ago (Dec. 1, 1994)
Published	30 years, 8 months ago (Dec. 1, 1994)
Published Print	30 years, 8 months ago (Dec. 1, 1994)

Funders 0

None

BibTeX

@article{Gander_1994, title={Least-squares fitting of circles and ellipses}, volume={34}, ISSN={1572-9125}, url={http://dx.doi.org/10.1007/bf01934268}, DOI={10.1007/bf01934268}, number={4}, journal={BIT}, publisher={Springer Science and Business Media LLC}, author={Gander, Walter and Golub, Gene H. and Strebel, Rolf}, year={1994}, month=dec, pages={558–578} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        20
      ]
    ],
    "date-time": "2025-08-20T12:47:07Z",
    "timestamp": 1755694027129
  },
  "reference-count": 17,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "4",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1994,
            12,
            1
          ]
        ],
        "date-time": "1994-12-01T00:00:00Z",
        "timestamp": 786240000000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "http://www.springer.com/tdm"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1994,
        12
      ]
    ]
  },
  "DOI": "10.1007/bf01934268",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        7,
        31
      ]
    ],
    "date-time": "2005-07-31T01:06:07Z",
    "timestamp": 1122771967000
  },
  "page": "558-578",
  "source": "Crossref",
  "is-referenced-by-count": 652,
  "title": "Least-squares fitting of circles and ellipses",
  "prefix": "10.1007",
  "volume": "34",
  "author": [
    {
      "given": "Walter",
      "family": "Gander",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "Gene H.",
      "family": "Golub",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Rolf",
      "family": "Strebel",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "297",
  "reference": [
    {
      "key": "BF01934268_CR1",
      "doi-asserted-by": "crossref",
      "unstructured": "V. Pratt,Direct Least Squares Fitting of Algebraic Surfaces, ACM J. Computer Graphics, Volume 21, Number 4, July 1987.",
      "DOI": "10.1145/37402.37420"
    },
    {
      "key": "BF01934268_CR2",
      "series-title": "Technical Report NPL DITC 211/92",
      "volume-title": "Strategies for Testing Assessment Software",
      "author": "M. G. Cox",
      "year": "1992",
      "unstructured": "M. G. Cox, A. B. Forbes,Strategies for Testing Assessment Software, Technical Report NPL DITC 211/92, National Physical Laboratory, Teddington, UK., 1992."
    },
    {
      "key": "BF01934268_CR3",
      "volume-title": "Matrix Computations",
      "author": "G. H. Golub",
      "year": "1989",
      "unstructured": "G. H. Golub, Ch. Van Loan,Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, MD., 1989.",
      "edition": "2nd ed."
    },
    {
      "key": "BF01934268_CR4",
      "doi-asserted-by": "crossref",
      "first-page": "293",
      "DOI": "10.1524/teme.1992.59.78.293",
      "volume": "59",
      "author": "D. Sourlier",
      "year": "1992",
      "unstructured": "D. Sourlier, A. Bucher,Normgerechter Best-fit-Algorithms f\u00fcr Freiform-Fl\u00e4chen oder andere nicht-regul\u00e4re Ausgleichs-Fl\u00e4chen in Parameter-Form, Technisches Messen 59 (1992), pp. 293\u2013302.",
      "journal-title": "Technisches Messen"
    },
    {
      "key": "BF01934268_CR5",
      "doi-asserted-by": "crossref",
      "first-page": "441",
      "DOI": "10.1007/BF01389650",
      "volume": "48",
      "author": "H. Sp\u00e4th",
      "year": "1986",
      "unstructured": "H. Sp\u00e4th,Orthogonal least squares fitting with linear manifolds, Numer. Math., 48 (1986), pp. 441\u2013445.",
      "journal-title": "Numer. Math."
    },
    {
      "key": "BF01934268_CR6",
      "doi-asserted-by": "crossref",
      "DOI": "10.2172/4779098",
      "volume-title": "The use of man-machine interaction in data fitting problems",
      "author": "L. B. Smith",
      "year": "1969",
      "unstructured": "L. B. Smith,The use of man-machine interaction in data fitting problems, TR CS 131, Computer Science Department, Stanford University, Stanford, CA, Ph.D. thesis, March 1969."
    },
    {
      "key": "BF01934268_CR7",
      "volume-title": "Method of least squares and principles of the theory of observations",
      "author": "Y. V. Linnik",
      "year": "1961",
      "unstructured": "Y. V. Linnik,Method of least squares and principles of the theory of observations, Pergamon Press, New York, 1961."
    },
    {
      "key": "BF01934268_CR8",
      "volume-title": "Contributions to the theory of linear least maximum approximation",
      "author": "C. L. Lawson",
      "year": "1961",
      "unstructured": "C. L. Lawson,Contributions to the theory of linear least maximum approximation, UCLA, Los Angeles, Ph.D. thesis, 1961."
    },
    {
      "key": "BF01934268_CR9",
      "doi-asserted-by": "crossref",
      "first-page": "56",
      "DOI": "10.1016/0146-664X(79)90082-0",
      "volume": "9",
      "author": "Fred L. Bookstein",
      "year": "1979",
      "unstructured": "Fred L. Bookstein,Fitting conic sections to scattered data, Computer Graphics and Image Processing 9, (1979), pp. 56\u201371.",
      "journal-title": "Computer Graphics and Image Processing"
    },
    {
      "issue": "2",
      "key": "BF01934268_CR10",
      "doi-asserted-by": "crossref",
      "first-page": "413",
      "DOI": "10.1137/0710036",
      "volume": "10",
      "author": "G. H. golub",
      "year": "1973",
      "unstructured": "G. H. golub, V. Pereyra,The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate, SIAM J. Numer. Anal. 10, No. 2, (1973), pp. 413\u2013432.",
      "journal-title": "SIAM J. Numer. Anal."
    },
    {
      "key": "BF01934268_CR11",
      "doi-asserted-by": "crossref",
      "unstructured": "M. Heidari, P. C. Heigold,Determination of Hydraulic Conductivity Tensor Using a Nonlinear Least Squares Estimator, Water Resources Bulletin, June 1993, pp. 415\u2013424.",
      "DOI": "10.1111/j.1752-1688.1993.tb03219.x"
    },
    {
      "key": "BF01934268_CR12",
      "doi-asserted-by": "crossref",
      "unstructured": "W. Gander, U. von Matt,Some Least Squares Problems, in Solving Problems in Scientific Computing Using Maple and Matlab, W. Gander and J. H\u0159eb\u00ed\u010dek, eds., Springer-Verlag, 1993, pp. 251\u2013266.",
      "DOI": "10.1007/978-3-642-97533-2"
    },
    {
      "key": "BF01934268_CR13",
      "doi-asserted-by": "crossref",
      "first-page": "1052",
      "DOI": "10.1137/0908085",
      "volume": "8",
      "author": "Paul T. Boggs",
      "year": "1987",
      "unstructured": "Paul T. Boggs, Richard H. Byrd and Robert B. Schnabel,A stable and efficient algorithm for nonlinear orthogonal distance regression, SIAM J. Sci. and Statist. Comput. 8 (1987), pp. 1052\u20131078.",
      "journal-title": "SIAM J. Sci. and Statist. Comput."
    },
    {
      "key": "BF01934268_CR14",
      "doi-asserted-by": "crossref",
      "DOI": "10.6028/NIST.IR.4834",
      "volume-title": "User's Reference Guide for ODRPACK Verion 2.01\u2014Software for Weighted Orthogonal Distance Regression",
      "author": "Paul T. Boggs",
      "year": "1992",
      "unstructured": "Paul T. Boggs, Richard H. Byrd, Janet E. Rogers and Robert B. Schnabel,User's Reference Guide for ODRPACK Verion 2.01\u2014Software for Weighted Orthogonal Distance Regression, National Institute of Standards and Technology, Gaithersburg, June 1992."
    },
    {
      "key": "BF01934268_CR15",
      "volume-title": "Practical Optimization",
      "author": "P. E. Gill",
      "year": "1981",
      "unstructured": "P. E. Gill, W. Murray and M. H. Wright,Practical Optimization, Academic Press, New York, 1981."
    },
    {
      "key": "BF01934268_CR16",
      "doi-asserted-by": "crossref",
      "first-page": "317",
      "DOI": "10.1016/0024-3795(87)90114-5",
      "volume": "88/89",
      "author": "Gene H. Golub",
      "year": "1987",
      "unstructured": "Gene H. Golub, Alan Hoffman, G. W. Stewart,A generalization of the Eckart-Young-Mirsky Matrix Approximation Theorem, Linear Algebra Appl., 88/89 (1987), pp. 317\u2013327.",
      "journal-title": "Linear Algebra Appl."
    },
    {
      "key": "BF01934268_CR17",
      "unstructured": "Walter Gander, Gene H. Golub, and Rolf Strebel,Fitting of circles and ellipses\u2014least squares solution, Technical Report 217, Insitiut f\u00fcr Wisenschaftliches Rechnen, ETH Z\u00fcrich, June 1994. Available via anonymous ftp from fip.inf.ethz.ch as doc/tech-reports/1994/217.ps."
    }
  ],
  "container-title": "BIT",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01934268.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/article/10.1007/BF01934268/fulltext.html",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "http://link.springer.com/content/pdf/10.1007/BF01934268",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2020,
        4,
        8
      ]
    ],
    "date-time": "2020-04-08T13:10:37Z",
    "timestamp": 1586351437000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "http://link.springer.com/10.1007/BF01934268"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1994,
        12
      ]
    ]
  },
  "references-count": 17,
  "journal-issue": {
    "issue": "4",
    "published-print": {
      "date-parts": [
        [
          1994,
          12
        ]
      ]
    }
  },
  "alternative-id": [
    "BF01934268"
  ],
  "URL": "http://dx.doi.org/10.1007/BF01934268",
  "relation": {},
  "ISSN": [
    "0006-3835",
    "1572-9125"
  ],
  "subject": [],
  "container-title-short": "BIT",
  "published": {
    "date-parts": [
      [
        1994,
        12
      ]
    ]
  }
}