Bibliography for Hermite Polynomial Interpolation

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  1. Geometric Hermite interpolation for space curves
    Xu, L.; Shi, J.
    Computer Aided Geometric Design, 2001, vol. 18, no. ER9, pp. 817-829, Ingenta.   
  2. Explicit Expression on Generalized Hermite Interpolation Basic Function
    Sun, H.-b.; Xi, M.-c.
    Journal- China University of Science and Technology, 2001, vol. 31, no. 4, pp. 419-424, Ingenta.   
  3. On using low-order Hermite interpolation in `direct dynamics' calculations of vibrational energies using the code `MULTIMODE'
    Carter, S.; Bowman, J. M.; Braams, B. J.
    Chemical Physics Letters, 2001, vol. 342, no. ER5-6, pp. 636-642, Ingenta.   
  4. On shape preserving C2 Hermite interpolation
    Manni, C.
    Bit, 2001, vol. 41, no. 1, pp. 127-148, Ingenta.   
  5. Hermite polynomials. In memory of Gian-Carlo Rota   
    Fisk, Steve
    J. Combin. Theory Ser. A 91 (2000), no. 1-2, 334--336, MathSciNet.  
  6. The Lebesgue function for generalized Hermite-Fejer interpolation on the Chebyshev nodes
    Byrne, G. J.; Mills, T. M.; Smith, S. J.
    Anziam Journal, 2000, vol. 42, no. 1, pp. 98-109, Ingenta.   
  7. On Hermite Interpolation.
    Shi, Ying Guang
    Journal of approximation theory, 2000, vol. 105, no. 1, pp. 49, Ingenta.   
  8. Approximation of orthogonal polynomials in terms of Hermite polynomials. Dedicated to Richard A. Askey on the occasion of his 65th birthday, Part II.   
    Lopez, Jose L.; Temme, Nico M.  
    Methods Appl. Anal. 6 (1999), no. 2, 131--146, MathSciNet.  
  9. Evaluation of some integrals involving Hermite polynomials.   
    Galua, Leda
    Math. Balkanica (N.S.) 13 (1999), no. 3-4, 377--384, MathSciNet.  
  10. On the Positivity of the Fundamental Polynomials for Generalized Hermite-Fejer Interpolation on the Chebyshev Nodes.
    Smith, Simon J.
    Journal of approximation theory, 1999, vol. 96, no. 2, pp. 338, Ingenta.   
  11. Error Estimates and Convergence Rates for Variational Hermite Interpolation.
    Luo, Zuhua; Levesley, Jeremy
    Journal of approximation theory, 1998, vol. 95, no. 2, pp. 264, Ingenta.   
  12. Matrix Expression of Hermite Interpolation Polynomials.
    Kida, S.; Trimandalawati, E.; Ogawa, S.
    Computers & mathematics with applications, 1997, vol. 33, no. 11, pp. 11, Ingenta.   
  13. A Generalization of Hermite Interpolation.
    Sun, Xie-Hua; Xie, Tingfan
    International journal of mathematics and mathema, 1997, vol. 20, no. 4, pp. 719, Ingenta.   
  14. Trigonometric Wavelets for Hermite Interpolation  
    Ewald Quak  
    Mathematics of Computation, Vol. 65, No. 214. (Apr., 1996), pp. 683-722, Jstor.  
  15. Geometric Hermite interpolation with maximal order and smoothness.
    Hollig, K.; Koch, J.
    Computer aided geometric design, 1996, vol. 13, no. 8, pp. 681, Ingenta.   
  16. Bivariate Hermite Interpolation and Numerical Curves.
    Gevorgian, Hovik V.; Hakopian, Hakop A.; Sahakian, Arthur A.
    Journal of approximation theory, 1996, vol. 85, no. 3, pp. 297, Ingenta.   
  17. Hermite Interpolation by Pythagorean Hodograph Quintics  
    R. T. Farouki, C. A. Neff  
    Mathematics of Computation, Vol. 64, No. 212. (Oct., 1995), pp. 1589-1609, Jstor.  
  18. Geometric Hermite interpolation.
    Hollig, K.; Koch, J.
    Computer aided geometric design, 1995, vol. 12, no. 6, pp. 567, Ingenta.   
  19. On the Bivariate Hermite Interpolation Problem.
    Gevorgian, H.V.; Hakopian, H.A.; Sahakian, A.A.
    Constructive approximation, 1995, vol. 11, no. 1, pp. 23, Ingenta.   
  20. Generalized Hermite Interpolation Via Matrix-Valued Conditionally Positive Definite Functions  
    Francis J. Narcowich, Joseph D. Ward  
    Mathematics of Computation, Vol. 63, No. 208. (Oct., 1994), pp. 661-687, Jstor.  
  21. Cardinal Hermite Spline Interpolation with Shifted Nodes  
    Gerlind Plonka, Manfred Tasche  
    Mathematics of Computation, Vol. 63, No. 208. (Oct., 1994), pp. 645-659, Jstor.  
  22. H1-Norm Error Bounds for Piecewise Hermite Bicubic Orthogonal Spline Collocation Schemes for Elliptic Boundary Value Problems  
    Bernard Bialecki, Xiao-Chuan Cai  
    SIAM Journal on Numerical Analysis, Vol. 31, No. 4. (Aug., 1994), pp. 1128-1146, Jstor.  
  23. Comparison of Lagrange interpolation and Hermite-Fejer type interpolation of higher order.
    Yingguang, Shi
    Acta mathematica scientia, 1994, vol. 14, no. 1, pp. 9, Ingenta.   
  24. A note on Hermite-Fejer interpolation on equidistant nodes.
    Mills, T.M.; Smith, J.A.
    Acta mathematica Hungarica, 1994, vol. 63, no. 1, pp. 45, Ingenta.   
  25. Quasi-Newton Method by Hermite Interpolation.
    Sturm, T. F.
    Journal of optimization theory and applications, 1994, vol. 83, no. 3, pp. 587, Ingenta.   
  26. Mean Convergence of Hermite Interpolation.
    Nevai, Paul; Xu, Yuan
    Journal of approximation theory, 1994, vol. 77, no. 3, pp. 282, Ingenta.   
  27. A Fast Domain Decomposition Poisson Solver on a Rectangle for Hermite Bicubic Orthogonal Spline Collocation  
    Bernard Bialecki  
    SIAM Journal on Numerical Analysis, Vol. 30, No. 2. (Apr., 1993), pp. 425-434, Jstor.  
  28. An addition formula for Hermite polynomials. (Russian)
    Viskov, O. V.
    Dokl. Akad. Nauk 330 (1993), no. 1,12--14 translation in Russian Acad. Sci. Dokl. Math. 47 (1993), no. 3, 366--370, MathSciNet.  
  29. Truncated Hermite interpolation polynomials.
    Vertesi, P.; Xu, Y.
    Studia scientiarum mathematicarum Hungarica, 1993, vol. 28, no. 1/2, pp. 203, Ingenta.   
  30. Hermite interpolation with trigonometric polynomials.
    Delvos, F.-J.
    BIT, 1993, no. 1, pp. 113, Ingenta.   
  31. On Hermite-Fejer interpolation on the Chebyshev nodes.
    Byrne, Graeme J.; Mills, T.M.; Smith, Simon J.
    Bulletin of the Australian Mathematical Society, 1993, vol. 47, no. 1, pp. 13, Ingenta.   
  32. Positive Hermite Interpolation by Quadratic Splines.
    Lahtinen, Aatos
    SIAM journal on mathematical analysis, 1993, vol. 24, no. 1, pp. 223, Ingenta.   
  33. Exploring Hermite Interpolation with Mathematica  
    Clifford A. Reiter
    PRIMUS, Vol. II, No. 2, (1992), pp. 173-182.  
  34. Efficient Algorithms for Periodic Hermite Spline Interpolation  
    G. Plonka, M. Tasche  
    Mathematics of Computation, Vol. 58, No. 198. (Apr., 1992), pp. 693-703, Jstor.  
  35. Fast Direct Solvers for Piecewise Hermite Bicubic Orthogonal Spline Collocation Equations  
    Bernard Bialecki, Graeme Fairweather, Karin R. Bennett  
    SIAM Journal on Numerical Analysis, Vol. 29, No. 1. (Feb., 1992), pp. 156-173, Jstor.  
  36. A family of Hermite interpolants by bisection algorithms.
    Merrien, J.-L.
    Numer. Algorithms 2 (1992), no. 2, 187--200, Math. Sci. Net.  
  37. On reduced n-cubic spline interpolation of Hermite type.
    Lenard, Margit
    Publicationes mathematicae, 1992, vol. 41, no. 3/4, pp. 243, Ingenta.   
  38. A new representation for the error function for the Hermite interpolation and sharper pointwise and uniform error bounds for the derivatives.
    Wong, P.J.Y.; Agarwal, R.P.
    Nonlinear analysis, 1992, vol. 19, no. 8, pp. 769, Ingenta.   
  39. Lagrange and Hermite Interpolation by Bivariate Splines.
    Nurnberger, G.; Riessinger, Th.
    Numerical functional analysis and optimization, 1992, vol. 13, no. 1/2, pp. 75, Ingenta.   
  40. Algebraic Surface Design with Hermite Interpolation.
    Bajaj, Chanderjit L.; Ihm, Insung
    ACM transactions on graphics, 1992, vol. 11, no. 1, pp. 61, Ingenta.   
  41. On Hermite-Fejer Interpolation in a Jordan Domain  
    Charles K. Chui, Xie-Chang Shen  
    Transactions of the American Mathematical Society, Vol. 323, No. 1. (Jan., 1991), pp. 93-109, Jstor.  
  42. A remark on Hermite-Lagrange interpolation   
    Ramharter, Gerhard   
    J. Approx. Theory 66 (1991), no. 1, 109--113
  43. Sharp Hermite interpolation error bounds for derivatives.
    Agarwal, R.P.
    Nonlinear analysis, 1991, vol. 17, no. 8, pp. 773, Ingenta.   
  44. On speed of mean convergence of Lagrange and Hermite interpolation based on the roots of Laguerre polynomials.
    Balazs, K.; Joo, I.
    Publicationes mathematicae, 1991, vol. 38, no. 3/4, pp. 247, Ingenta.   
  45. Runge-Kutta Defect Control Using Hermite-Birkhoff Interpolation.
    Higham, Desmond J.
    Siam journal on scientific and statistical compu, 1991, vol. 12, no. 5, pp. 991, Ingenta.   
  46. On the order of convergence of simultaneous approximation by Lagrange-Hermite interpolation.
    Kilgore, T.; Prestin, J.
    Mathematische Nachrichten, 1991, vol. 150, pp. 143, Ingenta.   
  47. Hermite Type Interpolation of Squared-Magnitude Functions.
    Lepschy, A.; Mian, G.A.; Viaro, U.
    Applied mathematics and computation, 1991, vol. 43, no. 3, pp. 265, Ingenta.   
  48. The Barycentric Approach Hermite Interpolation.
    Schneider, C.; Werner, W.
    Computing, 1991, vol. 46f1, pp. 35, Ingenta.   
  49. Cardinal hermite interpolation with box splines II.
    Riemenschneider, S.; Scherer, K.
    Numerische Mathematik, 1991, vol. 58, no. 6, pp. 591, Ingenta.   
  50. Nonnegativity-, Monotonicity-, or Convexity-Preserving Cubic and Quintic Hermite Interpolation  
    Randall L. Dougherty, Alan Edelman, James M. Hyman  
    Mathematics of Computation, Vol. 52, No. 186. (Apr., 1989), pp. 471-494, Jstor.  
  51. Conjectured Inequality for Hermite Interpolation at the Zeros of Jacobi Polynomials: Problem 87-7 (in Problems)  
    Walter Gautschi  
    SIAM Review, Vol. 29, No. 2. (Jun., 1987), pp. 297-298, Jstor.  
  52. A new characterization of Hermite polynomials  
    Varma, A. K.
    Acta Math. Hungar. 49 (1987), no. 1-2, 169--172, MathSciNet.  
  53. Hermite polynomial analysis of linear optimal control systems  
    Tsay, Yuh Feng; Lee, Tsu-Tian
    Internat. J. Systems Sci. 17 (1986), no. 12, 1751--1756, MathSciNet.  
  54. Properties of Hermite polynomials and their applications. (Russian)
    Approximate methods for analysis and their applications (Russian), 179--183,
    Vasileva, V. N.
    Akad. Nauk SSSR Sibirsk. Otdel., Ènerget. Inst., Irkutsk, 1985, MathSciNet.  
  55. Rodrigues' formulistic origins of certain generating functions for Hermite polynomials   
    Sultan, Taha Ibrahim
    J. Pure Math. 3 (1983), 103--109, MathSciNet.  
  56. The Budan-Fourier Theorem and Hermite-Birkhoff Spline Interpolation  
    T. N. T. Goodman, S. L. Lee  
    Transactions of the American Mathematical Society, Vol. 271, No. 2. (Jun., 1982), pp. 451-467, Jstor.  
  57. Hermite-Birkhoff Interpolation in the nth Roots of Unity
    A. S. Cavaretta, Jr., A. Sharma, R. S. Varga  
    Transactions of the American Mathematical Society, Vol. 259, No. 2. (Jun., 1980), pp. 621-628, Jstor.  
  58. Cardinal Hermite Spline Interpolation: Convergence as the Degree Tends to Infinity  
    M. J. Marsden, S. D. Riemenschneider  
    Transactions of the American Mathematical Society, Vol. 235. (Jan., 1978), pp. 221-244, Jstor.  
  59. The Trigonometric Hermite-Birkhoff Interpolation Problem  
    Darell J. Johnson  
    Transactions of the American Mathematical Society, Vol. 212. (Oct., 1975), pp. 365-374, Jstor.  
  60. Remarks on the Rank of Hermite-Birkhoff Interpolation  
    B. L. Chalmers, D. J. Johnson, F. T. Metcalf, G. D. Taylor  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 2. (Apr., 1974), pp. 254-259, Jstor.  
  61. Computation of Hermite Polynomials  
    Laurance C. Eisenhart, George E. Trapp, Jr.  
    Mathematics of Computation, Vol. 27, No. 123. (Jul., 1973), pp. 625-632, Jstor.  
  62. The Lagrange interpolation process with nodes at the roots of Hermite polynomials. (Russian)  
    Névai, G. P.   
    Acta Math. Acad. Sci. Hungar. 24 (1973), 209--213.
  63. Generating function and integral representation of Hermite polynomials in physical problems.
    Dvorák, S.
    Czechoslovak J. Phys. 23B (1973), 1281--1285, MathSciNet.  
  64. Computation of Hermite polynomials  
    Eisenhart, Laurance C.; Trapp, George E., Jr.
    Math. Comp. 27 (1973), 625--632.
  65. Integral properties of Hermite polynomials by operator methods
    Witschel, Wolfgang  
    Z. Angew. Math. Phys. 24 (1973), 861--870, MathSciNet.  
  66. On applications of Hermite polynomials  
    Shah, Manilal   
    METU J. Pure Appl. Sci. 4 (1971), no. 3, 221--235, MathSciNet.  
  67. Hermite-Birkhoff Interpolation Problems with Complex Nodes  
    Murray Schechter  
    American Mathematical Monthly, Vol. 76, No. 10. (Dec., 1969), pp. 1119-1122, Jstor.  
  68. A Partial Characterization of Poised Hermite-Birkhoff Interpolation Problems  
    K. Atkinson, A. Sharma  
    SIAM Journal on Numerical Analysis, Vol. 6, No. 2. (Jun., 1969), pp. 230-235, Jstor.  
  69. On Abel-Hermite-Birkhoff Interpolation  
    A. Sharma, J. Prasad  
    SIAM Journal on Numerical Analysis, Vol. 5, No. 4. (Dec., 1968), pp. 864-881, Jstor.  
  70. On an n-th order differential equation and Hermite polynomials.
    Chatterjea, S. K.
    Yokohama Math. J. 16 1968 75--76, MathSciNet.  
  71. Heat conduction and Hermite polynomials.
    Bhonsle, B. R.
    Proc. Nat. Acad. Sci. India Sect. A 36 1966 359--360, MathSciNet.  
  72. On Lagrange-Hermite Interpolation  
    J. F. Traub  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 12, No. 4. (Dec., 1964), pp. 886-891, Jstor.  
  73. A Bivariate Generalization of Hermite's Interpolation Formula  
    A. C. Ahlin  
    Mathematics of Computation, Vol. 18, No. 86. (Apr., 1964), pp. 264-273, Jstor.  
  74. On Hermite polynomials  
    Chatterjea, S. K.
    Rev. Mat. Hisp.-Amer. (4) 21 1961 85--92, MathSciNet.  
  75. A Generalization of Hermite's Interpolation Formula  
    A. Spitzbart
    American Mathematical Monthly, Vol. 67, No. 1. (Jan., 1960), pp. 42-46, Jstor.
  76. Heat equation and Hermite polynomials   
    Kampé de Fériet, J.
    Calcutta Math. Soc. Golden Jubilee Commemoration Vol. (1958/59), Part I pp. 193--204 Calcutta Math. Soc., Calcutta, MathSciNet.  
  77. Another Note on Hermite Polynomials (in Mathematical Notes)  
    M. P. Drazin  
    American Mathematical Monthly, Vol. 64, No. 2. (Feb., 1957), pp. 89-91, Jstor.  
  78. A Note on Hermite Polynomials (in Mathematical Notes)  
    L. Carlitz  
    American Mathematical Monthly, Vol. 62, No. 9. (Nov., 1955), pp. 646-647, Jstor.  
  79. The Expansion of a Function in Terms of its Values and Derivatives at Several Points  
    W. R. Andress  
    American Mathematical Monthly, Vol. 60, No. 6. (Jun. - Jul., 1953), pp. 394-396, Jstor.
  80. Convergence of expansions in the Hermite polynomials   
    Ikenberry, E.; Rutledge, W. A.
    J. Math. Physics 31, (1952). 180--183, MathSciNet.  
  81. Zeros of the Hermite polynomials and weights for Gauss' mechanical quadrature formula.
    Greenwood, Robert E.; Miller, J. J.
    Bull. Amer. Math. Soc. 54, (1948), MathSciNet.  
  82. On Interpolation II: On the Distribution of the Fundamental Points of Lagrange and Hermite Interpolation  
    P. Erdos, P. Turan  
    The Annals of Mathematics, 2nd Ser., Vol. 39, No. 4. (Oct., 1938), pp. 703-724, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003