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Volumn 20, Issue 1, 1994, Pages 21-62

Algorithm 726: ORTHPOL–A Package of Routines for Generating Orthogonal Polynomials and Gauss-Type Quadrature Rules

Author keywords

Gauss type quadrature rules; orthogonal polynomials

Indexed keywords

POLYNOMIALS; SOFTWARE ENGINEERING;

EID: 0028388229     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/174603.174605     Document Type: Article
Times cited : (240)

References (51)
  • 1
    • 0003283056 scopus 로고
    • Handbook of mathematical functions
    • EDS., U.S. Government Printing Office, Washington, D.C.
    • ABRAMOWITZ, M., AND STEGUN, I. A., EDS. 1964. Handbook of mathematical functions. NBS Appl. Math. Ser. 55, U.S. Government Printing Office, Washington, D.C.
    • (1964) NBS Appl. Math. Ser. 55
    • ABRAMOWITZ, M.1    STEGUN, I.A.2
  • 2
    • 0000964853 scopus 로고
    • A survey of matrix inverse eigenvalue problems
    • BOLEY, D., AND GOLUB, G. H. 1987. A survey of matrix inverse eigenvalue problems. Inverse Problems 3, 4, 595-622.
    • (1987) Inverse Problems , vol.3 , Issue.4 , pp. 595-622
    • BOLEY, D.1    GOLUB, G.H.2
  • 3
    • 0001937414 scopus 로고
    • Sur l'interpolation par la méthode des moindres carrés
    • 1-24. (Oeuvres I, pp. 473-498.)
    • CHEBYSHEV, P. L. 1859. Sur l'interpolation par la méthode des moindres carrés. Mém. Acad. Impér. Sci. St. Pétersbourg (7) 1, 15, 1-24. (Oeuvres I, pp. 473-498.)
    • (1859) Mém. Acad. Impér. Sci. St. Pétersbourg , vol.1 , Issue.7 , pp. 15
    • CHEBYSHEV, P.L.1
  • 4
    • 0004165067 scopus 로고
    • An Introduction to Orthogonal Polynomials
    • Gordon and Breach, New York.
    • CHIHARA, T. S. 1978. An Introduction to Orthogonal Polynomials. Gordon and Breach, New York.
    • (1978)
    • CHIHARA, T.S.1
  • 5
    • 0000235008 scopus 로고
    • Orthogonal polynomials and measures with end point masses
    • CHIHARA, T. S. 1985. Orthogonal polynomials and measures with end point masses. Rocky Mountain J. Math. 15, 3, 705-719.
    • (1985) Rocky Mountain J. Math. , vol.15 , Issue.3 , pp. 705-719
    • CHIHARA, T.S.1
  • 6
    • 84943473262 scopus 로고
    • Über die Gau βische Quadratur und eine Verallgemeinerung derselben
    • (Ges. Math. Abhandlungen I, pp. 65-87.)
    • CHRISTOFFEL, E. B. 1858. Über die Gau βische Quadratur und eine Verallgemeinerung derselben. J. Reme Angew. Math 55, 61-82. (Ges. Math. Abhandlungen I, pp. 65-87.)
    • (1858) J. Reme Angew. Math , vol.55 , pp. 61-82
    • CHRISTOFFEL, E.B.1
  • 7
    • 0008518813 scopus 로고
    • Sur une classe particulière de fonctions entières et de fractions continues
    • (Ges. Math. Abhandlungen II, pp. 42-50.)
    • CHRISTOFFEL, E. B. 1877. Sur une classe particulière de fonctions entières et de fractions continues. Ann. Mat. Pura Appl. Ser. 2, vol. 8, 1-10. (Ges. Math. Abhandlungen II, pp. 42-50.)
    • (1877) Ann. Mat. Pura Appl. Ser. , vol.2 , Issue.8 , pp. 1-10
    • CHRISTOFFEL, E.B.1
  • 8
    • 84968504266 scopus 로고
    • Chebyshev approximations for the natural logarithm of the gamma function
    • (Apr.)
    • CODY, W. J., AND HILLSTROM, K. E. 1967. Chebyshev approximations for the natural logarithm of the gamma function. Math. Comput 21, 98 (Apr.), 198-203.
    • (1967) Math. Comput , vol.21 , Issue.98 , pp. 198-203
    • CODY, W.J.1    HILLSTROM, K.E.2
  • 10
    • 0000912674 scopus 로고
    • The numerically stable reconstruction of a Jacobi matrix from spectral data
    • (Sept.)
    • DE BOOR, C., AND GOLUB, G. H. 1978. The numerically stable reconstruction of a Jacobi matrix from spectral data. Linear Algebra Appl. 21, 3 (Sept.), 245-260.
    • (1978) Linear Algebra Appl. , vol.21 , Issue.3 , pp. 245-260
    • DE BOOR, C.1    GOLUB, G.H.2
  • 11
    • 0040938577 scopus 로고
    • Moment-preserving spline approximation on finite intervals
    • (Mar.)
    • FRONTINI, M., GAUTSCHI, W., AND MILOVANOVIC, G. V. 1987. Moment-preserving spline approximation on finite intervals. Numer. Math. 50, 5 (Mar.), 503-518.
    • (1987) Numer. Math. , vol.50 , Issue.5 , pp. 503-518
    • FRONTINI, M.1    GAUTSCHI, W.2    MILOVANOVIC, G.V.3
  • 13
    • 84968490637 scopus 로고
    • An implementation of Christoffel's theorem in the theory of orthogonal polynomials
    • (Jan.)
    • GALANT, D. 1971. An implementation of Christoffel's theorem in the theory of orthogonal polynomials. Math. Comput. 25, 113 (Jan.), 111-113.
    • (1971) Math. Comput. , vol.25 , Issue.113 , pp. 111-113
    • GALANT, D.1
  • 14
    • 84968467316 scopus 로고
    • Algebraic methods for modified orthogonal polynomials
    • (Oct.)
    • GALANT, D. 1992. Algebraic methods for modified orthogonal polynomials. Math. Comput. 59, 200 (Oct.), 541-546.
    • (1992) Math. Comput. , vol.59 , Issue.200 , pp. 541-546
    • GALANT, D.1
  • 15
    • 0003805382 scopus 로고
    • Numerical quadrature in the presence of a singularity
    • (Sept.)
    • GAUTSCHI, W. 1967a. Numerical quadrature in the presence of a singularity. SIAM J. Numer. Anal. 4, 3 (Sept.), 357-362.
    • (1967) SIAM J. Numer. Anal. , vol.4 , Issue.3 , pp. 357-362
    • GAUTSCHI, W.1
  • 16
    • 0002334558 scopus 로고
    • Computational aspects of three-term recurrence relations
    • (Jan.)
    • GAUTSCHI, W. 1967b. Computational aspects of three-term recurrence relations. SIAM Rev. 9, 1 (Jan.), 24-82.
    • (1967) SIAM Rev. , vol.9 , Issue.1 , pp. 24-82
    • GAUTSCHI, W.1
  • 17
    • 84968507660 scopus 로고
    • On the preceding paper “A Legendre polynomial integral” by James L. Blue
    • (Apr.)
    • GAUTSCHI, W. 1979. On the preceding paper “A Legendre polynomial integral” by James L. Blue. Math. Comput. 33, 146 (Apr.), 742-743.
    • (1979) Math. Comput. , vol.33 , Issue.146 , pp. 742-743
    • GAUTSCHI, W.1
  • 18
    • 84966208168 scopus 로고
    • Minimal solutions of three-term recurrence relations and orthogonal polynomials
    • (Apr.)
    • GAUTSCHI, W. 1981. Minimal solutions of three-term recurrence relations and orthogonal polynomials. Math. Comput. 36, 154 (Apr.), 547-554.
    • (1981) Math. Comput. , vol.36 , Issue.154 , pp. 547-554
    • GAUTSCHI, W.1
  • 19
    • 0001505159 scopus 로고
    • On generating orthogonal polynomials
    • (Sept.)
    • GAUTSCHI, W. 1982a. On generating orthogonal polynomials. SIAM J. Sci. Stat. Comput. 3, 3 (Sept.), 289-317.
    • (1982) SIAM J. Sci. Stat. Comput. , vol.3 , Issue.3 , pp. 289-317
    • GAUTSCHI, W.1
  • 20
    • 0001849258 scopus 로고
    • An algorithmic implementation of the generalized Christoffel theorem
    • G. Hämmerlin, Ed. International Series of Numerical Mathematics, Birkhäuser, Basel
    • GAUTSCHI, W. 1982b. An algorithmic implementation of the generalized Christoffel theorem. In Numerical Integration, G. Hämmerlin, Ed. International Series of Numerical Mathematics, vol. 57. Birkhäuser, Basel, pp. 89-106.
    • (1982) In Numerical Integration , vol.57 , pp. 89-106
    • GAUTSCHI, W.1
  • 21
    • 0039752541 scopus 로고
    • Discrete approximations to spherically symmetric distributions
    • (June)
    • GAUTSCHI, W. 1984a. Discrete approximations to spherically symmetric distributions. Numer. Math. 44, 1 (June), 53-60.
    • (1984) Numer. Math. , vol.44 , Issue.1 , pp. 53-60
    • GAUTSCHI, W.1
  • 22
    • 0012411229 scopus 로고
    • Questions of numerical condition related to polynomials
    • G. H. Golub, Ed. Studies in Numerical Analysis. Mathematical Association of America, Washington, D.C.
    • GAUTSCHI, W. 1984b. Questions of numerical condition related to polynomials. In Studies in Mathematics, vol. 24. G. H. Golub, Ed. Studies in Numerical Analysis. Mathematical Association of America, Washington, D.C., pp. 140-177.
    • (1984) In Studies in Mathematics , vol.24 , pp. 140-177
    • GAUTSCHI, W.1
  • 23
    • 0008495563 scopus 로고
    • On the sensitivity of orthogonal polynomials to perturbations in the moments
    • (Apr.)
    • GAUTSCHI, W. 1986a. On the sensitivity of orthogonal polynomials to perturbations in the moments. Numer. Math. 48, 4 (Apr.), 369-382.
    • (1986) Numer. Math. , vol.48 , Issue.4 , pp. 369-382
    • GAUTSCHI, W.1
  • 24
    • 84976776224 scopus 로고
    • Reminiscences of my involvement in de Branges's proof of the Bieberbach conjecture
    • Mathematical Surveys and Monographs, no. 21. American Mathematical Society, Providence, R.I.
    • GAUTSCHI, W. 1986b. Reminiscences of my involvement in de Branges's proof of the Bieberbach conjecture. In The Bieberbach Conjecture. Mathematical Surveys and Monographs, no. 21. American Mathematical Society, Providence, R.I., pp. 205-211.
    • (1986) In The Bieberbach Conjecture. , pp. 205-211
    • GAUTSCHI, W.1
  • 25
    • 0008490343 scopus 로고
    • Computational aspects of orthogonal polynomials
    • P. Nevai, Ed. NATO ASI Series, Series C: Mathematical and Physical Sciences, vol. 294. Kluwer, Dordrecht
    • GAUTSCHI, W. 1990. Computational aspects of orthogonal polynomials. In Orthogonal Polynomials-Theory and Practice, P. Nevai, Ed. NATO ASI Series, Series C: Mathematical and Physical Sciences, vol. 294. Kluwer, Dordrecht, pp. 181-216.
    • (1990) In Orthogonal Polynomials-Theory and Practice , pp. 181-216
    • GAUTSCHI, W.1
  • 26
    • 84966217251 scopus 로고
    • A class of slowly convergent series and their summation by Gaussian quadrature
    • (July)
    • GAUTSCHI, W. 1991a. A class of slowly convergent series and their summation by Gaussian quadrature. Math. Comput. 57, 195 (July), 309-324.
    • (1991) Math. Comput. , vol.57 , Issue.195 , pp. 309-324
    • GAUTSCHI, W.1
  • 27
    • 84966212955 scopus 로고
    • On certain slowly convergent series occurring in plate contact problems
    • (July)
    • GAUTSCHI, W. 1991b. On certain slowly convergent series occurring in plate contact problems. Math. Comput. 57, 195 (July), 325-338.
    • (1991) Math. Comput. , vol.57 , Issue.195 , pp. 325-338
    • GAUTSCHI, W.1
  • 28
    • 34249925916 scopus 로고
    • Quadrature formulae on half-infinite intervals
    • C
    • GAUTSCHI, W. 1991C. Quadrature formulae on half-infinite intervals. BIT 31, 3, 438-446.
    • (1991) BIT , vol.31 , Issue.3 , pp. 438-446
    • GAUTSCHI, W.1
  • 29
    • 0042468810 scopus 로고
    • Computational problems and applications of orthogonal polynomials
    • d, IMACS Annals on Computing and Applied Mathematics, Baltzer, Basel
    • GAUTSCHI, W. 1991d. Computational problems and applications of orthogonal polynomials. In Orthogonal Polynomials and Their Applications. IMACS Annals on Computing and Applied Mathematics, vol. 9. Baltzer, Basel, pp. 61-71.
    • (1991) In Orthogonal Polynomials and Their Applications. , vol.9 , pp. 61-71
    • GAUTSCHI, W.1
  • 30
    • 0002539172 scopus 로고
    • Gauss-type quadrature rules for rational functions
    • H. Brass and G. Hämmerlin, Eds. International Series of Numerical Mathematics, vol. 112. Birhäuser, Basel
    • GAUTSCHI, W. 1993a. Gauss-type quadrature rules for rational functions. In Numerical Integration IV, H. Brass and G. Hämmerlin, Eds. International Series of Numerical Mathematics, vol. 112. Birhäuser, Basel, 111-130.
    • (1993) In Numerical Integration IV , pp. 111-130
    • GAUTSCHI, W.1
  • 31
    • 0027544727 scopus 로고
    • On the computation of generalized Fermi-Dirac and Bose-Einstein integrals
    • (Feb.)
    • GAUTSCHI, W. 1993b. On the computation of generalized Fermi-Dirac and Bose-Einstein integrals. Comput. Phys. Commun. 74, 2 (Feb.), 233-238.
    • (1993) Comput. Phys. Commun. , vol.74 , Issue.2 , pp. 233-238
    • GAUTSCHI, W.1
  • 32
    • 17544377846 scopus 로고
    • Is the recurrence relation for orthogonal polynomials always stable?
    • c
    • GAUTSCHI, W. 1993c. Is the recurrence relation for orthogonal polynomials always stable? BIT 33, 2, 277-284.
    • (1993) BIT , vol.33 , Issue.2 , pp. 277-284
    • GAUTSCHI, W.1
  • 33
    • 0041698994 scopus 로고
    • A set of orthogonal polynomials induced by a given orthogonal polynomial
    • (Aug.)
    • GAUTSCHI, W., AND LI, S. 1993. A set of orthogonal polynomials induced by a given orthogonal polynomial. Aequationes Math. 46, 1/2 (Aug.), 174-198.
    • (1993) Aequationes Math. , vol.46 , Issue.1-2 , pp. 174-198
    • GAUTSCHI, W.1    LI, S.2
  • 34
    • 84966211238 scopus 로고
    • Gaussian quadrature involving Einstein and Fermi functions with an application to summation of series
    • (Jan)
    • GAUTSCHI, W., AND MILOVANOVC, G. V. 1985. Gaussian quadrature involving Einstein and Fermi functions with an application to summation of series. Math Comput. 44, 169 (Jan), 177-190.
    • (1985) Math Comput. , vol.44 , Issue.169 , pp. 177-190
    • GAUTSCHI, W.1    MILOVANOVC, G.V.2
  • 35
    • 0040344644 scopus 로고
    • Spline approximations to spherically symmetric distributions
    • (July)
    • GAUTSCHI, W., AND MILOVANOVIC, G. V. 1986. Spline approximations to spherically symmetric distributions. Numer. Math. 49, 2/3 (July), 111-121.
    • (1986) Numer. Math. , vol.49 , Issue.2-3 , pp. 111-121
    • GAUTSCHI, W.1    MILOVANOVIC, G.V.2
  • 36
    • 0021006614 scopus 로고
    • Error bounds for Gaussian quadrature of analytic functions
    • (Dec.)
    • GAUTSCHI, W., AND VARGA, R. S. 1983. Error bounds for Gaussian quadrature of analytic functions. SIAM J. Numer. Anal. 20, 6 (Dec.), 1170-1186.
    • (1983) SIAM J. Numer. Anal. , vol.20 , Issue.6 , pp. 1170-1186
    • GAUTSCHI, W.1    VARGA, R.S.2
  • 37
    • 0039469279 scopus 로고
    • Computing the Hilbert transform of a Jacobi weight function
    • GAUTSCHI, W., AND WIMP, J. 1987. Computing the Hilbert transform of a Jacobi weight function. BIT 27, 2, 203-215.
    • (1987) BIT , vol.27 , Issue.2 , pp. 203-215
    • GAUTSCHI, W.1    WIMP, J.2
  • 38
    • 0023542077 scopus 로고
    • The numerical evaluation of singular integrals with coth-kernel
    • GAUTSCHI, W., KOVACEVC, M. A., AND MILOVANOVIC, G. V. 1987. The numerical evaluation of singular integrals with coth-kernel. BIT 27, 3, 389-402.
    • (1987) BIT , vol.27 , Issue.3 , pp. 389-402
    • GAUTSCHI, W.1    KOVACEVC, M.A.2    MILOVANOVIC, G.V.3
  • 39
    • 0001070999 scopus 로고
    • Some modified matrix eigenvalue problems
    • (Apr.)
    • GOLUB, G. H. 1973. Some modified matrix eigenvalue problems. SIAM Rev. 15, 2 (Apr.), 318-334.
    • (1973) SIAM Rev. , vol.15 , Issue.2 , pp. 318-334
    • GOLUB, G.H.1
  • 40
    • 0000223746 scopus 로고
    • Calculation of Gauss quadrature rules
    • (Apr.)
    • GOLUB, G. H., AND WELSCH, J. H. 1969. Calculation of Gauss quadrature rules. Math. Comput. 23, 106 (Apr.), 221-230.
    • (1969) Math. Comput. , vol.23 , Issue.106 , pp. 221-230
    • GOLUB, G.H.1    WELSCH, J.H.2
  • 41
    • 0001190030 scopus 로고
    • The numerically stable reconstruction of Jacobi matrices from spectral data
    • (Sept)
    • GRAGG, W. B., AND HARROD, W. J. 1984. The numerically stable reconstruction of Jacobi matrices from spectral data. Numer. Math. 44, 3 (Sept), 317-335.
    • (1984) Numer. Math. , vol.44 , Issue.3 , pp. 317-335
    • GRAGG, W.B.1    HARROD, W.J.2
  • 42
    • 0039546363 scopus 로고
    • On the calculation of Jacobi matrices
    • (July)
    • KAUTSKY, J., AND GOLUB, G. H. 1983. On the calculation of Jacobi matrices. Linear Algebra Appl. 52-53 (July), 439-455.
    • (1983) Linear Algebra Appl. 52-53 , pp. 439-455
    • KAUTSKY, J.1    GOLUB, G.H.2
  • 43
    • 84966209219 scopus 로고
    • Mathematical Functions and Their Approximations
    • Academic Press, New York.
    • LUKE, Y. L. 1975. Mathematical Functions and Their Approximations. Academic Press, New York.
    • (1975)
    • LUKE, Y.L.1
  • 44
    • 84972496151 scopus 로고
    • Elliptic orthogonal polynomials
    • REES, C. J. 1945. Elliptic orthogonal polynomials. Duke Math J. 12, 173-187.
    • (1945) Duke Math J. , vol.12 , pp. 173-187
    • REES, C.J.1
  • 45
    • 0039715520 scopus 로고
    • On Jacobi rotation patterns
    • Proceedings of Symposia in Applied Mathematics, American Mathematical Society, Providence, R.I.
    • RUTISHAUSER, H. 1963. On Jacobi rotation patterns. In Experimental Arithmetic, High Speed Computing and Mathematics. Proceedings of Symposia in Applied Mathematics, vol. 15. American Mathematical Society, Providence, R.I., pp. 219-239.
    • (1963) In Experimental Arithmetic, High Speed Computing and Mathematics. , vol.15 , pp. 219-239
    • RUTISHAUSER, H.1
  • 46
    • 0000705414 scopus 로고
    • An algorithm for Gaussian quadrature given modified moments
    • (Mar.)
    • SACK, R. A., AND DONOVAN, A. F. 1972. An algorithm for Gaussian quadrature given modified moments. Numer. Math. 18, 5 (Mar.), 465-478.
    • (1972) Numer. Math. , vol.18 , Issue.5 , pp. 465-478
    • SACK, R.A.1    DONOVAN, A.F.2
  • 47
    • 0003430610 scopus 로고
    • Gaussian Quadrature Formulas
    • Prentice-Hall, Englewood Cliffs, N.J.
    • STROUD, A. H., AND SECREST, D 1966. Gaussian Quadrature Formulas Prentice-Hall, Englewood Cliffs, N.J.
    • (1966)
    • STROUD, A.H.1    SECREST, D.2
  • 48
    • 0008494658 scopus 로고
    • Relation between polynomials orthogonal with different weights
    • (In Russian.)
    • UVAROV, V. B. 1959. Relation between polynomials orthogonal with different weights. Dokl. Akad. Nauk SSSR 126, 1, 33-36. (In Russian.)
    • (1959) Dokl. Akad. Nauk SSSR , vol.126 , Issue.1 , pp. 33-36
    • UVAROV, V.B.1
  • 49
    • 0040443249 scopus 로고
    • The connection between systems of polynomials that are orthogonal with respect to different distribution functions
    • (In Russian.)
    • UVAROV, V. B. 1969. The connection between systems of polynomials that are orthogonal with respect to different distribution functions. Ž Vycisl. Mat. Mat. Fiz. 9, 6, 1253-1262. (In Russian.)
    • (1969) Ž Vycisl. Mat. Mat. Fiz. , vol.9 , Issue.6 , pp. 1253-1262
    • UVAROV, V.B.1
  • 50
    • 0000955005 scopus 로고
    • Modified moments and Gaussian quadrature
    • WHEELER, J. C. 1974. Modified moments and Gaussian quadrature. Rocky Mountain J. Math. 4, 2, 287-296.
    • (1974) Rocky Mountain J. Math. , vol.4 , Issue.2 , pp. 287-296
    • WHEELER, J.C.1
  • 51
    • 0003660674 scopus 로고
    • The Algebraic Eigenvalue Problem
    • Clarendon Press, Oxford.
    • WILKINSON, J. H. 1965. The Algebraic Eigenvalue Problem. Clarendon Press, Oxford.
    • (1965)
    • WILKINSON, J.H.1


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