DOI: 10.1145/355984.355989. LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares

LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares

10.1145/355984.355989

Crossref journal-article

Association for Computing Machinery (ACM)

ACM Transactions on Mathematical Software (320)

Bibliography

Paige, C. C., & Saunders, M. A. (1982). LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares. ACM Transactions on Mathematical Software, 8(1), 43â71.

Authors 2

Christopher C. Paige (first)
Michael A. Saunders (additional)

References 25 Referenced 3,391

BJORCK , A. Use of conjugate gradients for solving linear least squares problems . In Duff, I.S. (Ed.), Conjugate-Gradwnt Methods and Stmilar Techntques, Rep . AERE R-9636, Computer Science and Systems Division, AERE Harwell, England , 1979 , 48-71. BJORCK, A. Use of conjugate gradients for solving linear least squares problems. In Duff, I.S. (Ed.), Conjugate-Gradwnt Methods and Stmilar Techntques, Rep. AERE R-9636, Computer Science and Systems Division, AERE Harwell, England, 1979, 48-71. / Use of conjugate gradients for solving linear least squares problems by BJORCK A. (1979)
BJORCK , A , AND DUFF , I.S . A direct method for the solution of sparse linear least squares problems . Linear Algebra Appl. 34 ( 1980 ), 43 - 67 . BJORCK, A, AND DUFF, I.S. A direct method for the solution of sparse linear least squares problems. Linear Algebra Appl. 34 (1980), 43-67. (10.1016/0024-3795(80)90158-5) / Linear Algebra Appl. / A direct method for the solution of sparse linear least squares problems by BJORCK A (1980)
BJORCK , A , AND ELFVING , T. Accelerated projection methods for computing Pseudoinverse solutions of systems of linear equations. Res Rep. LITH-MAT-R-1978-5 , Dep. Mathematics , Linkoping Univ. , Linkoping, Sweden , 1978 . BJORCK, A, AND ELFVING, T. Accelerated projection methods for computing Pseudoinverse solutions of systems of linear equations. Res Rep. LITH-MAT-R-1978-5, Dep. Mathematics, Linkoping Univ., Linkoping, Sweden, 1978. / Dep. Mathematics by BJORCK A (1978)
CHEW , Y.T. Iterative methods for linear least-squares problems. Res. Rep. CS-75-04, Dep. of Computer Science, Univ. Waterloo, Waterloo , Ont. , Canada , 1975 . CHEW, Y.T. Iterative methods for linear least-squares problems. Res. Rep. CS-75-04, Dep. of Computer Science, Univ. Waterloo, Waterloo, Ont., Canada, 1975. / Ont. by CHEW Y.T. (1975)
ELFVING , T. On the conjugate gradient method for solving linear least-squares problems. Res. Rep. L1TH-MAT-R-1978-3 , Dep. Mathematics, Linkoping Univ., Link6ping , Sweden , 1978 . ELFVING, T. On the conjugate gradient method for solving linear least-squares problems. Res. Rep. L1TH-MAT-R-1978-3, Dep. Mathematics, Linkoping Univ., Link6ping, Sweden, 1978. / Dep. Mathematics, Linkoping Univ., Link6ping by ELFVING T. (1978)
FADDEEV , D.K. , AND FADDEEVA , V.N. Computational Methods of Linear Algebra , Freeman , London , 1963 . FADDEEV, D.K., AND FADDEEVA, V.N. Computational Methods of Linear Algebra, Freeman, London, 1963. / Computational Methods of Linear Algebra by FADDEEV D.K. (1963)
GEORGE , A , AND HEATH , M T . Solution of sparse linear least squares problems using Givens rotations . Linear Algebra Appl. 34 ( 1980 ), 69 - 83 . GEORGE, A, AND HEATH, M T. Solution of sparse linear least squares problems using Givens rotations. Linear Algebra Appl. 34 (1980), 69-83. (10.1016/0024-3795(80)90159-7) / Linear Algebra Appl. / Solution of sparse linear least squares problems using Givens rotations by GEORGE A (1980)
GOLUB , G.H . Numerical methods for solving linear least-squares problems . Numer. Math. 7 ( 1965 ), 206 - 216 . GOLUB, G.H. Numerical methods for solving linear least-squares problems. Numer. Math. 7 (1965), 206-216. (10.1007/BF01436075) / Numer. Math. / Numerical methods for solving linear least-squares problems by GOLUB G.H (1965)
GOLUB , G.H. , AND KAHAN , W . Calculating the singular values and pseudoinverse of a matrix . SIAM J. Numer. Anal. 2 ( 1965 ), 205 - 224 . GOLUB, G.H., AND KAHAN, W. Calculating the singular values and pseudoinverse of a matrix. SIAM J. Numer. Anal. 2 (1965), 205-224. / SIAM J. Numer. Anal. / Calculating the singular values and pseudoinverse of a matrix by GOLUB G.H. (1965)
HESTENES , M.R. , AND STIEFEL , E . Methods of conjugate gradients for solving linear systems J . Res. N.B.S. 49 ( 1952 ), 409 - 436 . HESTENES, M.R., AND STIEFEL, E. Methods of conjugate gradients for solving linear systems J. Res. N.B.S. 49 (1952), 409-436. / Res. N.B.S. / Methods of conjugate gradients for solving linear systems J by HESTENES M.R. (1952)
HOUSEHOLDER , A.S . Terminating and non-terminating iterations for solving linear systems . SIAM J. Appl. Math. 3 ( 1955 ), 67 - 72 . HOUSEHOLDER, A.S. Terminating and non-terminating iterations for solving linear systems. SIAM J. Appl. Math. 3 (1955), 67-72. (10.1137/0103005) / SIAM J. Appl. Math. / Terminating and non-terminating iterations for solving linear systems by HOUSEHOLDER A.S (1955)
KENNEDY , W.J. , AND GENTLE , J.E. Stat~stwal Computing . Marcel Dekker, Inc. , New York and Basel, 1980 . KENNEDY, W.J., AND GENTLE, J.E. Stat~stwal Computing. Marcel Dekker, Inc., New York and Basel, 1980. / Stat~stwal Computing by KENNEDY W.J. (1980)
LANCZOS , C . An iteration method for the solution of the eigenvalue problem of linear differential and integral operators . J Res. N.B.S. 45 ( 1950 ), 255 - 282 . LANCZOS, C. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J Res. N.B.S. 45 (1950), 255-282. / J Res. N.B.S. / An iteration method for the solution of the eigenvalue problem of linear differential and integral operators by LANCZOS C (1950)
LE wis, J. G. Algorithms for sparse matrix eigenvalue problems. Res. Rep. STAN-CS-77-595 , Stanford Univ. , Stanford, CA , 1977 . LEwis, J.G. Algorithms for sparse matrix eigenvalue problems. Res. Rep. STAN-CS-77-595, Stanford Univ., Stanford, CA, 1977. / Stanford Univ. by LE (1977)
NASHED , M.Z. Aspects of generalized inverses in analysis and regularization . In Nashed, M.A. (Ed.), Generahzed Inverses and Applwat~ons , Academic Press , New York , 1976 , 193-244. NASHED, M.Z. Aspects of generalized inverses in analysis and regularization. In Nashed, M.A. (Ed.), Generahzed Inverses and Applwat~ons, Academic Press, New York, 1976, 193-244. / Generahzed Inverses and Applwat~ons by NASHED M.Z. (1976)
NELDER , J.A. GLIMM anual. Numerical Algorithms Group , 13 Banbury Road , Oxford, England , 1975 NELDER, J.A. GLIMManual. Numerical Algorithms Group, 13 Banbury Road, Oxford, England, 1975 / 13 Banbury Road by NELDER J.A. (1975)
PAIGE , C.C . Bidiagonahzatlon of matrices and solution of linear equations . SIAM J. Numer. Anal. 11 ( 1974 ), 197 - 209 . PAIGE, C.C. Bidiagonahzatlon of matrices and solution of linear equations. SIAM J. Numer. Anal. 11 (1974), 197-209. (10.1137/0711019) / SIAM J. Numer. Anal. / Bidiagonahzatlon of matrices and solution of linear equations by PAIGE C.C (1974)
PAIGE , C.C . Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix . J. Inst. Maths. Appl 18 ( 1976 ), 341 - 349 . PAIGE, C.C. Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix. J. Inst. Maths. Appl 18 (1976), 341-349. (10.1093/imamat/18.3.341) / J. Inst. Maths. Appl / Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix by PAIGE C.C (1976)
PAIGE , C.C. , AND SAUNDERS , M.A. Solution of sparse indefinite systems of equations and leastsquares problems Res. Rep. STAN-CS-73-399 , Stanford Univ. , Stanford, CA , 1973 . PAIGE, C.C., AND SAUNDERS, M.A. Solution of sparse indefinite systems of equations and leastsquares problems Res. Rep. STAN-CS-73-399, Stanford Univ., Stanford, CA, 1973. / Stanford Univ. by PAIGE C.C. (1973)
PAIGE , C.C. , AND SAUNDERS , M.A . Solution of sparse indefinite systems of linear equations . SIAM J. Numer. Anal. 12 ( 1975 ), 617 - 629 . PAIGE, C.C., AND SAUNDERS, M.A. Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12 (1975), 617-629. (10.1137/0712047) / SIAM J. Numer. Anal. / Solution of sparse indefinite systems of linear equations by PAIGE C.C. (1975)
PAIGE , C.C. , AND SAUNDERS , M.A. A bidiagonalization algorithm for sparse linear equations and least-squares problems. Rep. SOL 78-19 , Dep. Operations Research , Stanford Univ. , Stanford, CA , 1978 . PAIGE, C.C., AND SAUNDERS, M.A. A bidiagonalization algorithm for sparse linear equations and least-squares problems. Rep. SOL 78-19, Dep. Operations Research, Stanford Univ., Stanford, CA, 1978. / Dep. Operations Research by PAIGE C.C. (1978)
PAIGE C.C. AND SAUNDERS M.A. LSQR' Sparse hnear equations and least-squares problems. ACM Trans. Math. Softw. to appear. 10.1145/355993.356000 PAIGE C.C. AND SAUNDERS M.A. LSQR' Sparse hnear equations and least-squares problems. ACM Trans. Math. Softw. to appear. 10.1145/355993.356000
STEWART , G.W. Research, development and LINPACK . In Rice, J.R. (Ed.), Mathematwal Software III , Academic Press , New York , 1977 , pp. 1 - 14 . STEWART, G.W. Research, development and LINPACK. In Rice, J.R. (Ed.), Mathematwal Software III, Academic Press, New York, 1977, pp. 1-14. / Mathematwal Software III by STEWART G.W. (1977)
VAN HEIJST , J. , JACOBS , J. , AND SCHERDERS , J. Kleinste-kwadraten problemen. Dep. Mathematics Rep ., Eindhoven University of Technology , Eindhoven, The Netherlands, August 1976 VAN HEIJST, J., JACOBS, J., AND SCHERDERS, J. Kleinste-kwadraten problemen. Dep. Mathematics Rep., Eindhoven University of Technology, Eindhoven, The Netherlands, August 1976 / Kleinste-kwadraten problemen. Dep. Mathematics Rep by VAN HEIJST J. (1976)
WILKINSON , J.H. The Algebraw Etgenvalue Problem . Oxford University Press (Clarendon) , New York , 1965 . WILKINSON, J.H. The Algebraw Etgenvalue Problem. Oxford University Press (Clarendon), New York, 1965. / The Algebraw Etgenvalue Problem by WILKINSON J.H. (1965)

Dates

Type	When
Created	23 years ago (July 27, 2002, 7:29 a.m.)
Deposited	2 months, 1 week ago (June 17, 2025, 2:07 p.m.)
Indexed	18 minutes ago (Aug. 26, 2025, 11:51 p.m.)
Issued	43 years, 5 months ago (March 1, 1982)
Published	43 years, 5 months ago (March 1, 1982)
Published Online	43 years, 5 months ago (March 1, 1982)
Published Print	43 years, 5 months ago (March 1, 1982)

Funders 0

None

BibTeX

@article{Paige_1982, title={LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares}, volume={8}, ISSN={1557-7295}, url={http://dx.doi.org/10.1145/355984.355989}, DOI={10.1145/355984.355989}, number={1}, journal={ACM Transactions on Mathematical Software}, publisher={Association for Computing Machinery (ACM)}, author={Paige, Christopher C. and Saunders, Michael A.}, year={1982}, month=mar, pages={43–71} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        27
      ]
    ],
    "date-time": "2025-08-27T03:51:13Z",
    "timestamp": 1756266673505,
    "version": "3.41.0"
  },
  "reference-count": 25,
  "publisher": "Association for Computing Machinery (ACM)",
  "issue": "1",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1982,
            3,
            1
          ]
        ],
        "date-time": "1982-03-01T00:00:00Z",
        "timestamp": 383788800000
      },
      "content-version": "vor",
      "delay-in-days": 0,
      "URL": "https://www.acm.org/publications/policies/copyright_policy#Background"
    }
  ],
  "content-domain": {
    "domain": [
      "dl.acm.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1982,
        3
      ]
    ]
  },
  "DOI": "10.1145/355984.355989",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        27
      ]
    ],
    "date-time": "2002-07-27T11:29:03Z",
    "timestamp": 1027769343000
  },
  "page": "43-71",
  "update-policy": "https://doi.org/10.1145/crossmark-policy",
  "source": "Crossref",
  "is-referenced-by-count": 3391,
  "title": "LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares",
  "prefix": "10.1145",
  "volume": "8",
  "author": [
    {
      "given": "Christopher C.",
      "family": "Paige",
      "sequence": "first",
      "affiliation": [
        {
          "name": "School of Computer Science, McGill University, Montreal, P.Q., Canada H3C 3G1"
        }
      ]
    },
    {
      "given": "Michael A.",
      "family": "Saunders",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Operations Research, Stanford University, Stanford, CA"
        }
      ]
    }
  ],
  "member": "320",
  "published-online": {
    "date-parts": [
      [
        1982,
        3
      ]
    ]
  },
  "reference": [
    {
      "key": "e_1_2_1_1_2",
      "volume-title": "Use of conjugate gradients for solving linear least squares problems",
      "author": "BJORCK A.",
      "year": "1979",
      "unstructured": "BJORCK , A. Use of conjugate gradients for solving linear least squares problems . In Duff, I.S. (Ed.), Conjugate-Gradwnt Methods and Stmilar Techntques, Rep . AERE R-9636, Computer Science and Systems Division, AERE Harwell, England , 1979 , 48-71. BJORCK, A. Use of conjugate gradients for solving linear least squares problems. In Duff, I.S. (Ed.), Conjugate-Gradwnt Methods and Stmilar Techntques, Rep. AERE R-9636, Computer Science and Systems Division, AERE Harwell, England, 1979, 48-71."
    },
    {
      "key": "e_1_2_1_2_2",
      "doi-asserted-by": "crossref",
      "first-page": "43",
      "DOI": "10.1016/0024-3795(80)90158-5",
      "article-title": "A direct method for the solution of sparse linear least squares problems",
      "volume": "34",
      "author": "BJORCK A",
      "year": "1980",
      "unstructured": "BJORCK , A , AND DUFF , I.S . A direct method for the solution of sparse linear least squares problems . Linear Algebra Appl. 34 ( 1980 ), 43 - 67 . BJORCK, A, AND DUFF, I.S. A direct method for the solution of sparse linear least squares problems. Linear Algebra Appl. 34 (1980), 43-67.",
      "journal-title": "Linear Algebra Appl."
    },
    {
      "key": "e_1_2_1_3_2",
      "volume-title": "Dep. Mathematics",
      "author": "BJORCK A",
      "year": "1978",
      "unstructured": "BJORCK , A , AND ELFVING , T. Accelerated projection methods for computing Pseudoinverse solutions of systems of linear equations. Res Rep. LITH-MAT-R-1978-5 , Dep. Mathematics , Linkoping Univ. , Linkoping, Sweden , 1978 . BJORCK, A, AND ELFVING, T. Accelerated projection methods for computing Pseudoinverse solutions of systems of linear equations. Res Rep. LITH-MAT-R-1978-5, Dep. Mathematics, Linkoping Univ., Linkoping, Sweden, 1978."
    },
    {
      "key": "e_1_2_1_4_2",
      "volume-title": "Ont.",
      "author": "CHEW Y.T.",
      "year": "1975",
      "unstructured": "CHEW , Y.T. Iterative methods for linear least-squares problems. Res. Rep. CS-75-04, Dep. of Computer Science, Univ. Waterloo, Waterloo , Ont. , Canada , 1975 . CHEW, Y.T. Iterative methods for linear least-squares problems. Res. Rep. CS-75-04, Dep. of Computer Science, Univ. Waterloo, Waterloo, Ont., Canada, 1975."
    },
    {
      "key": "e_1_2_1_5_2",
      "volume-title": "Dep. Mathematics, Linkoping Univ., Link6ping",
      "author": "ELFVING T.",
      "year": "1978",
      "unstructured": "ELFVING , T. On the conjugate gradient method for solving linear least-squares problems. Res. Rep. L1TH-MAT-R-1978-3 , Dep. Mathematics, Linkoping Univ., Link6ping , Sweden , 1978 . ELFVING, T. On the conjugate gradient method for solving linear least-squares problems. Res. Rep. L1TH-MAT-R-1978-3, Dep. Mathematics, Linkoping Univ., Link6ping, Sweden, 1978."
    },
    {
      "key": "e_1_2_1_6_2",
      "volume-title": "Computational Methods of Linear Algebra",
      "author": "FADDEEV D.K.",
      "year": "1963",
      "unstructured": "FADDEEV , D.K. , AND FADDEEVA , V.N. Computational Methods of Linear Algebra , Freeman , London , 1963 . FADDEEV, D.K., AND FADDEEVA, V.N. Computational Methods of Linear Algebra, Freeman, London, 1963."
    },
    {
      "key": "e_1_2_1_7_2",
      "doi-asserted-by": "crossref",
      "first-page": "69",
      "DOI": "10.1016/0024-3795(80)90159-7",
      "article-title": "Solution of sparse linear least squares problems using Givens rotations",
      "volume": "34",
      "author": "GEORGE A",
      "year": "1980",
      "unstructured": "GEORGE , A , AND HEATH , M T . Solution of sparse linear least squares problems using Givens rotations . Linear Algebra Appl. 34 ( 1980 ), 69 - 83 . GEORGE, A, AND HEATH, M T. Solution of sparse linear least squares problems using Givens rotations. Linear Algebra Appl. 34 (1980), 69-83.",
      "journal-title": "Linear Algebra Appl."
    },
    {
      "key": "e_1_2_1_8_2",
      "doi-asserted-by": "crossref",
      "first-page": "206",
      "DOI": "10.1007/BF01436075",
      "article-title": "Numerical methods for solving linear least-squares problems",
      "volume": "7",
      "author": "GOLUB G.H",
      "year": "1965",
      "unstructured": "GOLUB , G.H . Numerical methods for solving linear least-squares problems . Numer. Math. 7 ( 1965 ), 206 - 216 . GOLUB, G.H. Numerical methods for solving linear least-squares problems. Numer. Math. 7 (1965), 206-216.",
      "journal-title": "Numer. Math."
    },
    {
      "key": "e_1_2_1_9_2",
      "first-page": "205",
      "article-title": "Calculating the singular values and pseudoinverse of a matrix",
      "volume": "2",
      "author": "GOLUB G.H.",
      "year": "1965",
      "unstructured": "GOLUB , G.H. , AND KAHAN , W . Calculating the singular values and pseudoinverse of a matrix . SIAM J. Numer. Anal. 2 ( 1965 ), 205 - 224 . GOLUB, G.H., AND KAHAN, W. Calculating the singular values and pseudoinverse of a matrix. SIAM J. Numer. Anal. 2 (1965), 205-224.",
      "journal-title": "SIAM J. Numer. Anal."
    },
    {
      "key": "e_1_2_1_10_2",
      "first-page": "409",
      "article-title": "Methods of conjugate gradients for solving linear systems J",
      "volume": "49",
      "author": "HESTENES M.R.",
      "year": "1952",
      "unstructured": "HESTENES , M.R. , AND STIEFEL , E . Methods of conjugate gradients for solving linear systems J . Res. N.B.S. 49 ( 1952 ), 409 - 436 . HESTENES, M.R., AND STIEFEL, E. Methods of conjugate gradients for solving linear systems J. Res. N.B.S. 49 (1952), 409-436.",
      "journal-title": "Res. N.B.S."
    },
    {
      "key": "e_1_2_1_11_2",
      "doi-asserted-by": "crossref",
      "first-page": "67",
      "DOI": "10.1137/0103005",
      "article-title": "Terminating and non-terminating iterations for solving linear systems",
      "volume": "3",
      "author": "HOUSEHOLDER A.S",
      "year": "1955",
      "unstructured": "HOUSEHOLDER , A.S . Terminating and non-terminating iterations for solving linear systems . SIAM J. Appl. Math. 3 ( 1955 ), 67 - 72 . HOUSEHOLDER, A.S. Terminating and non-terminating iterations for solving linear systems. SIAM J. Appl. Math. 3 (1955), 67-72.",
      "journal-title": "SIAM J. Appl. Math."
    },
    {
      "key": "e_1_2_1_12_2",
      "volume-title": "Stat~stwal Computing",
      "author": "KENNEDY W.J.",
      "year": "1980",
      "unstructured": "KENNEDY , W.J. , AND GENTLE , J.E. Stat~stwal Computing . Marcel Dekker, Inc. , New York and Basel, 1980 . KENNEDY, W.J., AND GENTLE, J.E. Stat~stwal Computing. Marcel Dekker, Inc., New York and Basel, 1980."
    },
    {
      "key": "e_1_2_1_13_2",
      "first-page": "255",
      "article-title": "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators",
      "volume": "45",
      "author": "LANCZOS C",
      "year": "1950",
      "unstructured": "LANCZOS , C . An iteration method for the solution of the eigenvalue problem of linear differential and integral operators . J Res. N.B.S. 45 ( 1950 ), 255 - 282 . LANCZOS, C. An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J Res. N.B.S. 45 (1950), 255-282.",
      "journal-title": "J Res. N.B.S."
    },
    {
      "key": "e_1_2_1_14_2",
      "volume-title": "Stanford Univ.",
      "author": "LE",
      "year": "1977",
      "unstructured": "LE wis, J. G. Algorithms for sparse matrix eigenvalue problems. Res. Rep. STAN-CS-77-595 , Stanford Univ. , Stanford, CA , 1977 . LEwis, J.G. Algorithms for sparse matrix eigenvalue problems. Res. Rep. STAN-CS-77-595, Stanford Univ., Stanford, CA, 1977."
    },
    {
      "key": "e_1_2_1_15_2",
      "volume-title": "Generahzed Inverses and Applwat~ons",
      "author": "NASHED M.Z.",
      "year": "1976",
      "unstructured": "NASHED , M.Z. Aspects of generalized inverses in analysis and regularization . In Nashed, M.A. (Ed.), Generahzed Inverses and Applwat~ons , Academic Press , New York , 1976 , 193-244. NASHED, M.Z. Aspects of generalized inverses in analysis and regularization. In Nashed, M.A. (Ed.), Generahzed Inverses and Applwat~ons, Academic Press, New York, 1976, 193-244."
    },
    {
      "key": "e_1_2_1_16_2",
      "volume-title": "13 Banbury Road",
      "author": "NELDER J.A.",
      "year": "1975",
      "unstructured": "NELDER , J.A. GLIMM anual. Numerical Algorithms Group , 13 Banbury Road , Oxford, England , 1975 NELDER, J.A. GLIMManual. Numerical Algorithms Group, 13 Banbury Road, Oxford, England, 1975"
    },
    {
      "key": "e_1_2_1_17_2",
      "doi-asserted-by": "crossref",
      "first-page": "197",
      "DOI": "10.1137/0711019",
      "article-title": "Bidiagonahzatlon of matrices and solution of linear equations",
      "volume": "11",
      "author": "PAIGE C.C",
      "year": "1974",
      "unstructured": "PAIGE , C.C . Bidiagonahzatlon of matrices and solution of linear equations . SIAM J. Numer. Anal. 11 ( 1974 ), 197 - 209 . PAIGE, C.C. Bidiagonahzatlon of matrices and solution of linear equations. SIAM J. Numer. Anal. 11 (1974), 197-209.",
      "journal-title": "SIAM J. Numer. Anal."
    },
    {
      "key": "e_1_2_1_18_2",
      "doi-asserted-by": "crossref",
      "first-page": "341",
      "DOI": "10.1093/imamat/18.3.341",
      "article-title": "Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix",
      "volume": "18",
      "author": "PAIGE C.C",
      "year": "1976",
      "unstructured": "PAIGE , C.C . Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix . J. Inst. Maths. Appl 18 ( 1976 ), 341 - 349 . PAIGE, C.C. Error analysis of the Lanczos algorithm for tridiagonalizing a symmetric matrix. J. Inst. Maths. Appl 18 (1976), 341-349.",
      "journal-title": "J. Inst. Maths. Appl"
    },
    {
      "key": "e_1_2_1_19_2",
      "volume-title": "Stanford Univ.",
      "author": "PAIGE C.C.",
      "year": "1973",
      "unstructured": "PAIGE , C.C. , AND SAUNDERS , M.A. Solution of sparse indefinite systems of equations and leastsquares problems Res. Rep. STAN-CS-73-399 , Stanford Univ. , Stanford, CA , 1973 . PAIGE, C.C., AND SAUNDERS, M.A. Solution of sparse indefinite systems of equations and leastsquares problems Res. Rep. STAN-CS-73-399, Stanford Univ., Stanford, CA, 1973."
    },
    {
      "key": "e_1_2_1_20_2",
      "doi-asserted-by": "crossref",
      "first-page": "617",
      "DOI": "10.1137/0712047",
      "article-title": "Solution of sparse indefinite systems of linear equations",
      "volume": "12",
      "author": "PAIGE C.C.",
      "year": "1975",
      "unstructured": "PAIGE , C.C. , AND SAUNDERS , M.A . Solution of sparse indefinite systems of linear equations . SIAM J. Numer. Anal. 12 ( 1975 ), 617 - 629 . PAIGE, C.C., AND SAUNDERS, M.A. Solution of sparse indefinite systems of linear equations. SIAM J. Numer. Anal. 12 (1975), 617-629.",
      "journal-title": "SIAM J. Numer. Anal."
    },
    {
      "key": "e_1_2_1_21_2",
      "volume-title": "Dep. Operations Research",
      "author": "PAIGE C.C.",
      "year": "1978",
      "unstructured": "PAIGE , C.C. , AND SAUNDERS , M.A. A bidiagonalization algorithm for sparse linear equations and least-squares problems. Rep. SOL 78-19 , Dep. Operations Research , Stanford Univ. , Stanford, CA , 1978 . PAIGE, C.C., AND SAUNDERS, M.A. A bidiagonalization algorithm for sparse linear equations and least-squares problems. Rep. SOL 78-19, Dep. Operations Research, Stanford Univ., Stanford, CA, 1978."
    },
    {
      "key": "e_1_2_1_22_2",
      "unstructured": "PAIGE C.C. AND SAUNDERS M.A. LSQR' Sparse hnear equations and least-squares problems. ACM Trans. Math. Softw. to appear. 10.1145/355993.356000   PAIGE C.C. AND SAUNDERS M.A. LSQR' Sparse hnear equations and least-squares problems. ACM Trans. Math. Softw. to appear. 10.1145/355993.356000"
    },
    {
      "key": "e_1_2_1_23_2",
      "first-page": "1",
      "volume-title": "Mathematwal Software III",
      "author": "STEWART G.W.",
      "year": "1977",
      "unstructured": "STEWART , G.W. Research, development and LINPACK . In Rice, J.R. (Ed.), Mathematwal Software III , Academic Press , New York , 1977 , pp. 1 - 14 . STEWART, G.W. Research, development and LINPACK. In Rice, J.R. (Ed.), Mathematwal Software III, Academic Press, New York, 1977, pp. 1-14."
    },
    {
      "key": "e_1_2_1_24_2",
      "volume-title": "Kleinste-kwadraten problemen. Dep. Mathematics Rep",
      "author": "VAN HEIJST J.",
      "year": "1976",
      "unstructured": "VAN HEIJST , J. , JACOBS , J. , AND SCHERDERS , J. Kleinste-kwadraten problemen. Dep. Mathematics Rep ., Eindhoven University of Technology , Eindhoven, The Netherlands, August 1976 VAN HEIJST, J., JACOBS, J., AND SCHERDERS, J. Kleinste-kwadraten problemen. Dep. Mathematics Rep., Eindhoven University of Technology, Eindhoven, The Netherlands, August 1976"
    },
    {
      "key": "e_1_2_1_25_2",
      "volume-title": "The Algebraw Etgenvalue Problem",
      "author": "WILKINSON J.H.",
      "year": "1965",
      "unstructured": "WILKINSON , J.H. The Algebraw Etgenvalue Problem . Oxford University Press (Clarendon) , New York , 1965 . WILKINSON, J.H. The Algebraw Etgenvalue Problem. Oxford University Press (Clarendon), New York, 1965."
    }
  ],
  "container-title": "ACM Transactions on Mathematical Software",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://dl.acm.org/doi/10.1145/355984.355989",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://dl.acm.org/doi/pdf/10.1145/355984.355989",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2025,
        6,
        17
      ]
    ],
    "date-time": "2025-06-17T18:07:58Z",
    "timestamp": 1750183678000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://dl.acm.org/doi/10.1145/355984.355989"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1982,
        3
      ]
    ]
  },
  "references-count": 25,
  "journal-issue": {
    "issue": "1",
    "published-print": {
      "date-parts": [
        [
          1982,
          3
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1145/355984.355989"
  ],
  "URL": "http://dx.doi.org/10.1145/355984.355989",
  "relation": {},
  "ISSN": [
    "0098-3500",
    "1557-7295"
  ],
  "subject": [],
  "container-title-short": "ACM Trans. Math. Softw.",
  "published": {
    "date-parts": [
      [
        1982,
        3
      ]
    ]
  },
  "assertion": [
    {
      "value": "1982-03-01",
      "order": 2,
      "name": "published",
      "label": "Published",
      "group": {
        "name": "publication_history",
        "label": "Publication History"
      }
    }
  ]
}