DOI: 10.1016/s0898-1221(00)00071-7. Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations

Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations

10.1016/s0898-1221(00)00071-7

Crossref journal-article

Elsevier BV

Computers & Mathematics with Applications (78)

Bibliography

Kansa, E. J., & Hon, Y. C. (2000). Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations. Computers & Mathematics with Applications, 39(7â8), 123â137.

Authors 2

E.J. Kansa (first)
Y.C. Hon (additional)

References 33 Referenced 339

10.1090/S0025-5718-1990-0993931-7 / Math. Comp. / Multivariable interpolation and conditionally positive definite functions II by Madych (1990)
{'key': '10.1016/S0898-1221(00)00071-7_BIB2', 'first-page': '181', 'article-title': 'Scattered data interpolation: Tests of some methods', 'volume': '38', 'author': 'Franke', 'year': '1972', 'journal-title': 'Math. Comput.'} / Math. Comput. / Scattered data interpolation: Tests of some methods by Franke (1972)
10.1029/JB076i008p01905 / J. Geophys. Res. / Multiquadric equations of topography and other irregular surfaces by Hardy (1971)
10.1016/0898-1221(90)90272-L / Computers Math. Applic. / Theory and applications of the multiquadric-biharmonic method: 20 years of discovery by Hardy (1990)
{'key': '10.1016/S0898-1221(00)00071-7_BIB5', 'series-title': 'Constructive Theory of Functions of Several Variables', 'article-title': 'Spline minimizing rotation-invariant seminorms in Sobolev space', 'volume': 'Volume 571', 'author': 'Duchon', 'year': '1977'} / Constructive Theory of Functions of Several Variables / Spline minimizing rotation-invariant seminorms in Sobolev space by Duchon (1977)
10.1016/0898-1221(90)90270-T / Computers Math. Applic. / Multiquadrics—A scattered data approximation scheme with applications to computational fluid dynamics—I. Surface approximations and partial derivative estimates by Kansa (1990)
10.1016/0898-1221(90)90271-K / Computers Math. Applic. / Multiquadrics—A scattered data approximation scheme with applications to computational fluid dynamics—II. Solutions to hyperbolic, parabolic, and elliptic partial differential equations by Kansa (1990)
10.1016/0096-3003(94)90099-X / Appl. Math. Comp. / The theory of radial basis functions used in the dual reciprocity boundary element method by Golberg (1994)
10.1016/S0096-3003(96)00109-9 / Appl. Math. Comput. / Applications of the multiquadric method for the solution of elliptic partial differential equations by Sharan (1997)
{'key': '10.1016/S0898-1221(00)00071-7_BIB10', 'series-title': 'Discrete projection methods for integral equations', 'author': 'Golberg', 'year': '1997'} / Discrete projection methods for integral equations by Golberg (1997)
10.1023/A:1025606420187 / Sci. Comput. / A multiquadric interpolation method for solving initial value problems by Hon (1997)
10.1016/S0096-3003(96)00309-8 / Appl. Math. Comput. / Multiquadric method for the numerical solution of a biphasic model by Hon (1997)
10.1016/S0096-3003(97)10060-1 / Appl. Math. Comput. / An efficient numerical scheme for Burgers equation by Hon (1998)
10.1061/(ASCE)0733-9429(1999)125:5(524) / ASCE J. Hydraulic Engineering / A multiquadric solution for shallow water equation by Hon (1999)
{'issue': '1', 'key': '10.1016/S0898-1221(00)00071-7_BIB15', 'first-page': '31', 'article-title': 'A radial basis function method for solving options pricing model', 'volume': '8', 'author': 'Hon', 'year': '1999', 'journal-title': 'Financial Engineering'} / Financial Engineering / A radial basis function method for solving options pricing model by Hon (1999)
10.1007/BF02836101 / Approximation Theory and its Application / Hermite-Bikhoff interpolation of scattered data by radial basis function by Wu (1992)
{'key': '10.1016/S0898-1221(00)00071-7_BIB17', 'series-title': 'Advances in Computational Mathematics', 'article-title': 'Solving PDE with radial basis function and the error estimation', 'volume': 'Volume 202', 'author': 'Wu', 'year': '1998'} / Advances in Computational Mathematics / Solving PDE with radial basis function and the error estimation by Wu (1998)
{'key': '10.1016/S0898-1221(00)00071-7_BIB18', 'series-title': 'Approaches to Numerical Relativity', 'author': 'Dubal', 'year': '1993'} / Approaches to Numerical Relativity by Dubal (1993)
{'key': '10.1016/S0898-1221(00)00071-7_BIB19', 'article-title': 'On unsymmetric collocation by radial basis functions', 'author': 'Schaback', 'year': '1999', 'journal-title': 'Appl. Math. Comput.'} / Appl. Math. Comput. / On unsymmetric collocation by radial basis functions by Schaback (1999)
{'key': '10.1016/S0898-1221(00)00071-7_BIB20', 'series-title': 'Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations', 'author': 'Smith', 'year': '1996'} / Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations by Smith (1996)
10.1002/nla.1680020208 / Numer. Lin. Algebra Applic. / Stability of block LU factorization by Demmel (1995)
{'issue': '1', 'key': '10.1016/S0898-1221(00)00071-7_BIB22', 'first-page': '146', 'article-title': 'Domain decomposition and local refinement for multiquadric approximations. I. Second-order equations in one-dimension', 'volume': '1', 'author': 'Dubal', 'year': '1994', 'journal-title': 'Int. J. Appl. Sci. Comput.'} / Int. J. Appl. Sci. Comput. / Domain decomposition and local refinement for multiquadric approximations. I. Second-order equations in one-dimension by Dubal (1994)
10.1016/0898-1221(92)90175-H / Computers Math. Applic. / Miscellaneous error bounds for multiquadric and related interpolants by Madych (1992)
{'key': '10.1016/S0898-1221(00)00071-7_BIB24', 'series-title': "A parametric study of Hardy's multiquadric equations for scattered data interpolation", 'author': 'Tarwater', 'year': '1985'} / A parametric study of Hardy's multiquadric equations for scattered data interpolation by Tarwater (1985)
10.1016/0898-1221(91)90123-L / Computers Math. Applic. / The parameter R2 in multiquadric interpolation by Carlson (1991)
{'issue': '2', 'key': '10.1016/S0898-1221(00)00071-7_BIB26', 'first-page': '319', 'article-title': 'An adaptive radial basis function approach to modeling scattered data', 'volume': '1', 'author': 'Milroy', 'year': '1994', 'journal-title': 'J. Appl. Sci. and Comput.'} / J. Appl. Sci. and Comput. / An adaptive radial basis function approach to modeling scattered data by Milroy (1994)
10.1016/S0955-7997(96)00033-1 / Engr. Anal. with Bound. Elem. / Improved multiquadric approximation for partial differential equations by Golberg (1996)
{'key': '10.1016/S0898-1221(00)00071-7_BIB28', 'first-page': '221', 'article-title': 'Radial basis function approximation of the surface wind field from scattered data', 'volume': '4', 'author': 'Hickernell', 'year': '1998', 'journal-title': 'Appl. Sci. Comput.'} / Appl. Sci. Comput. / Radial basis function approximation of the surface wind field from scattered data by Hickernell (1998)
10.1002/(SICI)1099-0887(199902)15:2<137::AID-CNM233>3.0.CO;2-9 / Comm. Numer. Meth. Engng / Boundary element methods using compactly supported radial basis functions by Chen (1999)
10.1007/BF02123482 / Adv. Comput. Math. / Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree by Wendland (1995)
10.1016/S0898-1221(99)00098-X / Computers Math. Applic. / Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme by Wong (1999)
10.1023/A:1018962112170 / Adv. Comp. Math. / Multistep approximations algorithms: Improved convergence rates through postconditioning with smoothing kernals by Fasshauer (1999)
10.1007/BF01893414 / Constr. Approx. / Interpolation of scattered data: Distance matrices and conditionally positive definite functions by Micchelli (1986)

Dates

Type	When
Created	22 years, 3 months ago (April 23, 2003, 3:57 p.m.)
Deposited	1 year, 7 months ago (Jan. 2, 2024, 3:26 a.m.)
Indexed	1 day, 8 hours ago (Aug. 20, 2025, 8:28 a.m.)
Issued	25 years, 4 months ago (April 1, 2000)
Published	25 years, 4 months ago (April 1, 2000)
Published Print	25 years, 4 months ago (April 1, 2000)

Funders 0

None

BibTeX

@article{Kansa_2000, title={Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations}, volume={39}, ISSN={0898-1221}, url={http://dx.doi.org/10.1016/s0898-1221(00)00071-7}, DOI={10.1016/s0898-1221(00)00071-7}, number={7–8}, journal={Computers & Mathematics with Applications}, publisher={Elsevier BV}, author={Kansa, E.J. and Hon, Y.C.}, year={2000}, month=apr, pages={123–137} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        20
      ]
    ],
    "date-time": "2025-08-20T12:28:01Z",
    "timestamp": 1755692881971
  },
  "reference-count": 33,
  "publisher": "Elsevier BV",
  "issue": "7-8",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2000,
            4,
            1
          ]
        ],
        "date-time": "2000-04-01T00:00:00Z",
        "timestamp": 954547200000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://www.elsevier.com/tdm/userlicense/1.0/"
    },
    {
      "start": {
        "date-parts": [
          [
            2013,
            7,
            17
          ]
        ],
        "date-time": "2013-07-17T00:00:00Z",
        "timestamp": 1374019200000
      },
      "content-version": "vor",
      "delay-in-days": 4855,
      "URL": "https://www.elsevier.com/open-access/userlicense/1.0/"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2000,
        4
      ]
    ]
  },
  "DOI": "10.1016/s0898-1221(00)00071-7",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2003,
        4,
        23
      ]
    ],
    "date-time": "2003-04-23T19:57:07Z",
    "timestamp": 1051127827000
  },
  "page": "123-137",
  "source": "Crossref",
  "is-referenced-by-count": 339,
  "title": "Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations",
  "prefix": "10.1016",
  "volume": "39",
  "author": [
    {
      "given": "E.J.",
      "family": "Kansa",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "Y.C.",
      "family": "Hon",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "78",
  "reference": [
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB1",
      "doi-asserted-by": "crossref",
      "first-page": "211",
      "DOI": "10.1090/S0025-5718-1990-0993931-7",
      "article-title": "Multivariable interpolation and conditionally positive definite functions II",
      "volume": "54",
      "author": "Madych",
      "year": "1990",
      "journal-title": "Math. Comp."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB2",
      "first-page": "181",
      "article-title": "Scattered data interpolation: Tests of some methods",
      "volume": "38",
      "author": "Franke",
      "year": "1972",
      "journal-title": "Math. Comput."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB3",
      "doi-asserted-by": "crossref",
      "first-page": "1905",
      "DOI": "10.1029/JB076i008p01905",
      "article-title": "Multiquadric equations of topography and other irregular surfaces",
      "volume": "76",
      "author": "Hardy",
      "year": "1971",
      "journal-title": "J. Geophys. Res."
    },
    {
      "issue": "8/9",
      "key": "10.1016/S0898-1221(00)00071-7_BIB4",
      "doi-asserted-by": "crossref",
      "first-page": "163",
      "DOI": "10.1016/0898-1221(90)90272-L",
      "article-title": "Theory and applications of the multiquadric-biharmonic method: 20 years of discovery",
      "volume": "19",
      "author": "Hardy",
      "year": "1990",
      "journal-title": "Computers Math. Applic."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB5",
      "series-title": "Constructive Theory of Functions of Several Variables",
      "article-title": "Spline minimizing rotation-invariant seminorms in Sobolev space",
      "volume": "Volume 571",
      "author": "Duchon",
      "year": "1977"
    },
    {
      "issue": "8/9",
      "key": "10.1016/S0898-1221(00)00071-7_BIB6",
      "doi-asserted-by": "crossref",
      "first-page": "127",
      "DOI": "10.1016/0898-1221(90)90270-T",
      "article-title": "Multiquadrics\u2014A scattered data approximation scheme with applications to computational fluid dynamics\u2014I. Surface approximations and partial derivative estimates",
      "volume": "19",
      "author": "Kansa",
      "year": "1990",
      "journal-title": "Computers Math. Applic."
    },
    {
      "issue": "8/9",
      "key": "10.1016/S0898-1221(00)00071-7_BIB7",
      "doi-asserted-by": "crossref",
      "first-page": "147",
      "DOI": "10.1016/0898-1221(90)90271-K",
      "article-title": "Multiquadrics\u2014A scattered data approximation scheme with applications to computational fluid dynamics\u2014II. Solutions to hyperbolic, parabolic, and elliptic partial differential equations",
      "volume": "19",
      "author": "Kansa",
      "year": "1990",
      "journal-title": "Computers Math. Applic."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB8",
      "doi-asserted-by": "crossref",
      "first-page": "125",
      "DOI": "10.1016/0096-3003(94)90099-X",
      "article-title": "The theory of radial basis functions used in the dual reciprocity boundary element method",
      "volume": "60",
      "author": "Golberg",
      "year": "1994",
      "journal-title": "Appl. Math. Comp."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB9",
      "doi-asserted-by": "crossref",
      "first-page": "275",
      "DOI": "10.1016/S0096-3003(96)00109-9",
      "article-title": "Applications of the multiquadric method for the solution of elliptic partial differential equations",
      "volume": "84",
      "author": "Sharan",
      "year": "1997",
      "journal-title": "Appl. Math. Comput."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB10",
      "series-title": "Discrete projection methods for integral equations",
      "author": "Golberg",
      "year": "1997"
    },
    {
      "issue": "1",
      "key": "10.1016/S0898-1221(00)00071-7_BIB11",
      "doi-asserted-by": "crossref",
      "first-page": "51",
      "DOI": "10.1023/A:1025606420187",
      "article-title": "A multiquadric interpolation method for solving initial value problems",
      "volume": "12",
      "author": "Hon",
      "year": "1997",
      "journal-title": "Sci. Comput."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB12",
      "doi-asserted-by": "crossref",
      "first-page": "153",
      "DOI": "10.1016/S0096-3003(96)00309-8",
      "article-title": "Multiquadric method for the numerical solution of a biphasic model",
      "volume": "88",
      "author": "Hon",
      "year": "1997",
      "journal-title": "Appl. Math. Comput."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB13",
      "doi-asserted-by": "crossref",
      "first-page": "37",
      "DOI": "10.1016/S0096-3003(97)10060-1",
      "article-title": "An efficient numerical scheme for Burgers equation",
      "volume": "95",
      "author": "Hon",
      "year": "1998",
      "journal-title": "Appl. Math. Comput."
    },
    {
      "issue": "5",
      "key": "10.1016/S0898-1221(00)00071-7_BIB14",
      "doi-asserted-by": "crossref",
      "first-page": "524",
      "DOI": "10.1061/(ASCE)0733-9429(1999)125:5(524)",
      "article-title": "A multiquadric solution for shallow water equation",
      "volume": "125",
      "author": "Hon",
      "year": "1999",
      "journal-title": "ASCE J. Hydraulic Engineering"
    },
    {
      "issue": "1",
      "key": "10.1016/S0898-1221(00)00071-7_BIB15",
      "first-page": "31",
      "article-title": "A radial basis function method for solving options pricing model",
      "volume": "8",
      "author": "Hon",
      "year": "1999",
      "journal-title": "Financial Engineering"
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB16",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1007/BF02836101",
      "article-title": "Hermite-Bikhoff interpolation of scattered data by radial basis function",
      "volume": "8",
      "author": "Wu",
      "year": "1992",
      "journal-title": "Approximation Theory and its Application"
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB17",
      "series-title": "Advances in Computational Mathematics",
      "article-title": "Solving PDE with radial basis function and the error estimation",
      "volume": "Volume 202",
      "author": "Wu",
      "year": "1998"
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB18",
      "series-title": "Approaches to Numerical Relativity",
      "author": "Dubal",
      "year": "1993"
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB19",
      "article-title": "On unsymmetric collocation by radial basis functions",
      "author": "Schaback",
      "year": "1999",
      "journal-title": "Appl. Math. Comput."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB20",
      "series-title": "Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations",
      "author": "Smith",
      "year": "1996"
    },
    {
      "issue": "2",
      "key": "10.1016/S0898-1221(00)00071-7_BIB21",
      "doi-asserted-by": "crossref",
      "first-page": "173",
      "DOI": "10.1002/nla.1680020208",
      "article-title": "Stability of block LU factorization",
      "volume": "2",
      "author": "Demmel",
      "year": "1995",
      "journal-title": "Numer. Lin. Algebra Applic."
    },
    {
      "issue": "1",
      "key": "10.1016/S0898-1221(00)00071-7_BIB22",
      "first-page": "146",
      "article-title": "Domain decomposition and local refinement for multiquadric approximations. I. Second-order equations in one-dimension",
      "volume": "1",
      "author": "Dubal",
      "year": "1994",
      "journal-title": "Int. J. Appl. Sci. Comput."
    },
    {
      "issue": "12",
      "key": "10.1016/S0898-1221(00)00071-7_BIB23",
      "doi-asserted-by": "crossref",
      "first-page": "121",
      "DOI": "10.1016/0898-1221(92)90175-H",
      "article-title": "Miscellaneous error bounds for multiquadric and related interpolants",
      "volume": "24",
      "author": "Madych",
      "year": "1992",
      "journal-title": "Computers Math. Applic."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB24",
      "series-title": "A parametric study of Hardy's multiquadric equations for scattered data interpolation",
      "author": "Tarwater",
      "year": "1985"
    },
    {
      "issue": "9",
      "key": "10.1016/S0898-1221(00)00071-7_BIB25",
      "doi-asserted-by": "crossref",
      "first-page": "29",
      "DOI": "10.1016/0898-1221(91)90123-L",
      "article-title": "The parameter R2 in multiquadric interpolation",
      "volume": "21",
      "author": "Carlson",
      "year": "1991",
      "journal-title": "Computers Math. Applic."
    },
    {
      "issue": "2",
      "key": "10.1016/S0898-1221(00)00071-7_BIB26",
      "first-page": "319",
      "article-title": "An adaptive radial basis function approach to modeling scattered data",
      "volume": "1",
      "author": "Milroy",
      "year": "1994",
      "journal-title": "J. Appl. Sci. and Comput."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB27",
      "doi-asserted-by": "crossref",
      "first-page": "9",
      "DOI": "10.1016/S0955-7997(96)00033-1",
      "article-title": "Improved multiquadric approximation for partial differential equations",
      "volume": "18",
      "author": "Golberg",
      "year": "1996",
      "journal-title": "Engr. Anal. with Bound. Elem."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB28",
      "first-page": "221",
      "article-title": "Radial basis function approximation of the surface wind field from scattered data",
      "volume": "4",
      "author": "Hickernell",
      "year": "1998",
      "journal-title": "Appl. Sci. Comput."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB29",
      "doi-asserted-by": "crossref",
      "first-page": "137",
      "DOI": "10.1002/(SICI)1099-0887(199902)15:2<137::AID-CNM233>3.0.CO;2-9",
      "article-title": "Boundary element methods using compactly supported radial basis functions",
      "volume": "15",
      "author": "Chen",
      "year": "1999",
      "journal-title": "Comm. Numer. Meth. Engng"
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB30",
      "doi-asserted-by": "crossref",
      "first-page": "389",
      "DOI": "10.1007/BF02123482",
      "article-title": "Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree",
      "volume": "4",
      "author": "Wendland",
      "year": "1995",
      "journal-title": "Adv. Comput. Math."
    },
    {
      "issue": "8",
      "key": "10.1016/S0898-1221(00)00071-7_BIB31",
      "doi-asserted-by": "crossref",
      "first-page": "23",
      "DOI": "10.1016/S0898-1221(99)00098-X",
      "article-title": "Multizone decomposition for simulation of time-dependent problems using the multiquadric scheme",
      "volume": "37",
      "author": "Wong",
      "year": "1999",
      "journal-title": "Computers Math. Applic."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB32",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1023/A:1018962112170",
      "article-title": "Multistep approximations algorithms: Improved convergence rates through postconditioning with smoothing kernals",
      "volume": "10",
      "author": "Fasshauer",
      "year": "1999",
      "journal-title": "Adv. Comp. Math."
    },
    {
      "key": "10.1016/S0898-1221(00)00071-7_BIB33",
      "doi-asserted-by": "crossref",
      "first-page": "11",
      "DOI": "10.1007/BF01893414",
      "article-title": "Interpolation of scattered data: Distance matrices and conditionally positive definite functions",
      "volume": "2",
      "author": "Micchelli",
      "year": "1986",
      "journal-title": "Constr. Approx."
    }
  ],
  "container-title": "Computers &amp; Mathematics with Applications",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0898122100000717?httpAccept=text/xml",
      "content-type": "text/xml",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://api.elsevier.com/content/article/PII:S0898122100000717?httpAccept=text/plain",
      "content-type": "text/plain",
      "content-version": "vor",
      "intended-application": "text-mining"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        1,
        2
      ]
    ],
    "date-time": "2024-01-02T08:26:27Z",
    "timestamp": 1704183987000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://linkinghub.elsevier.com/retrieve/pii/S0898122100000717"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2000,
        4
      ]
    ]
  },
  "references-count": 33,
  "journal-issue": {
    "issue": "7-8",
    "published-print": {
      "date-parts": [
        [
          2000,
          4
        ]
      ]
    }
  },
  "alternative-id": [
    "S0898122100000717"
  ],
  "URL": "http://dx.doi.org/10.1016/S0898-1221(00)00071-7",
  "relation": {},
  "ISSN": [
    "0898-1221"
  ],
  "subject": [],
  "container-title-short": "Computers &amp; Mathematics with Applications",
  "published": {
    "date-parts": [
      [
        2000,
        4
      ]
    ]
  }
}