Bibliography for Numerical Differentiation

unabridged

  1. Error formulas for divided difference expansions and numerical differentiation  
    Floater, Michael S.
    J. Approx. Theory  122  (2003),  no. 1, 1--9, MathSciNet.  
  2. Computer Derivations of Numerical Differentiation Formulae (Classroom Notes)  
    John Mathews  
    International Journal of Mathematics Education in Science and Technology, Volume 34 No 2 (March-April 2003), pp.280-287, Ingenta.  
  3. Generalized associated polynomials and their application in numerical differentiation and quadrature
    Skrzipek, M. R.
    Calcolo  40  (2003),  no. 3, 131--147, MathSciNet.  
  4. Stable numerical differentiation: when is it possible?
    Ramm, A. G.; Smirnova, A.
    Journal- Korea Society for Industrial and Applied Mathematics, 2003, vol. 7, no. 1, pp. 47-62, Ingenta.  
  5. Further Discussion on Numerical Differentiation and Numerical Integration Using Cubic Spline Function
    Sun, J.; Jin, H.; Cao, D.-x.
    Journal- China University of Mining and Technology, 2002, vol. 31, no. 1, pp. 103-106, Ingenta.  
  6. Discrete derivatives and symmetries of difference equations.    
    Levi, D.; Negro, J.; del Olmo, M. A.    
    J. Phys. A 34 (2001), no. 10, 2023--2030, MathSciNet.  
  7. Corrigendum to: "Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series"   
    Khan, Ishtiaq Rasool; Ohba, Ryoji    
    [J. Comput. Appl. Math. 107 (1999), no. 2, 179--193; MR 2000d:65020].    
    J. Comput. Appl. Math. 130 (2001), no. 1-2, 385, MathSciNet.  
  8. Generalized Numerical Differentiation in the Turbidity Spectrum Method
    Shmakov, S. L.
    Optics and Spectroscopy, 2001, vol. 91, no. 2, pp. 283-287, Ingenta.  
  9. Sharp Estimates for Errors of Numerical Differentiation Type Formulas on Trigonometric Polynomials
    Vinogradov, O. L.; Zhuk, V. V.
    Journal of Mathematical Sciences, 2001, vol. 105, no. 5, pp. 2347-2376, Ingenta.  
  10. On stable numerical differentiation
    Ramm, A. G.; Smirnova, A. B.
    Mathematics of Computation, 2001, vol. 70, no. 235, pp. 1131-1154, Ingenta.  
  11. Calculating the dynamic strain tensor field using modal analysis and numerical differentiation
    Sehlstedt, N.
    Journal of Sound and Vibration, 2001, vol. 244, no. 3, pp. 407-430, Ingenta.  
  12. Inverse Problems Light: Numerical Differentiation  
    Hanke, M.; Scherzer, O.  
    American Mathematical Monthly, 2001, vol. 108, no. 6, pp. 512-521, Ingenta.  
  13. New finite difference formulas for numerical differentiation.  
    Khan, Ishtiaq Rasool; Ohba, Ryoji   
    J. Comput. Appl. Math. 126 (2000), no. 1-2, 269--276, MathSciNet.  
  14. The generalized Richardson extrapolation process GREP and computation of derivatives of limits of sequences with applications to the [Graphics:../Images/NumericalDiffBib_gr_1.gif]-transformation.   
    Sidi, Avram
    Numerical analysis 2000, Vol. II: Interpolation and extrapolation. J. Comput. Appl. Math. 122 (2000), no. 1-2, 251--273, MathSciNet.  
  15. The trade-offs between alternative finite difference techniques used to price derivative securities.    
    Buetow, Gerald W.; Sochacki, James S.    
    Appl. Math. Comput. 115 (2000), no. 2-3, 177--190, MathSciNet.  
  16. An introduction to automatic differentiation.    
    Verma, Arun    
    Current Sci. 78 (2000), no. 7, 804--807, MathSciNet.  
  17. On numerical differentiation algorithms for nonlinear estimation
    Diop, S.; Grizzle, J. W.; Chaplais, F.
    IEEE Conference on Decision and Control, 2000, no. CONF39, pp. 1133-1138, Ingenta.  
  18. Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs
    Cash, J. R.
    Journal of Computational and Applied Mathematics, 2000, vol. 125, no. ER1-2, pp. 117-130, Ingenta.  
  19. Numerical differentiation for local and global tangent operators in computational plasticity.
    Perez-Foguet, A.; Rodriguez-Ferran, A.; Huerta, A.
    Computer Methods in Applied Mechanics and Engineering, 2000, vol. 189, no. 1, pp. 277, Ingenta.   
  20. Numerical differentiation for non-trivial consistent tangent matrices: an application to the MRS-Lade model.
    Perez-Foguet, A.; Rodriguez-Ferran, A.; Huerta, A.
    International Journal for Numerical Methods in Engineering, 2000, vol. 48, no. 2, pp. 159, Ingenta.   
  21. Numerical differentiation of implicitly defined curves.  
    Syam, Muhammed I.; Siyyam, Hani I.   
    J. Comput. Appl. Math. 108 (1999), no. 1-2, 131--144, MathSciNet.  
  22. Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series.    
    Khan, Ishtiaq Rasool; Ohba, Ryoji    
    J. Comput. Appl. Math. 107 (1999), no. 2, 179--193, MathSciNet.  
  23. Discrete-time implementation of high-gain observers for numerical differentiation.
    Dabroom, A.M.; Khalil, H.K.
    International journal of control, 1999, vol. 72, no. 17, pp. 1523, Ingenta.   
  24. For numerical differentiation, dimensionality can be a blessing!
    Anderssen, Robert S.; Hegland, Markus
    Mathematics of computation, 1999, vol. 68, no. 227, pp. 1121, Ingenta.   
  25. Automatic differentiation of numerical integration algorithms.
    Eberhard, Peter; Bischof, Christian
    Mathematics of computation, 1999, vol. 68, no. 226, pp. 717, Ingenta.   
  26. Discrete mollification and automatic numerical differentiation.    
    Murio, D. A.; Mejía, C. E.; Zhan, S.   
    Comput. Math. Appl. 35 (1998), no. 5, 1--16, MathSciNet.  
  27. Mesh adaption and automatic differentiation for optimal shape design.   
    Mohammadi, B.   
    Int. J. Comput. Fluid Dyn. 10 (1998), no. 3, 199--211, MathSciNet.  
  28. The efficient computation of sparse Jacobian matrices using automatic differentiation.   
    Coleman, Thomas F.; Verma, Arun   
    SIAM J. Sci. Comput. 19 (1998), no. 4, 1210--1233 (electronic), MathSciNet.  
  29. Using forward accumulation for automatic differentiation of implicitly-defined functions.    
    Bartholomew-Biggs, M. C.  
    Comput. Optim. Appl. 9 (1998), no. 1, 65--84, MathSciNet.  
  30. Estimating velocities and accelerations of animal locomotion: a simulation experiment comparing numerical differentiation algorithms.
    Walker, J. A.
    Journal of experimental biology, 1998, vol. 201, no. 7, pp. 981, Ingenta.   
  31. Discrete Mollification and Automatic Numerical Differentiation.
    Murio, D.A.; Mejia, C.E.; Zhan, S.
    Computers & mathematics with applications, 1998, vol. 35, no. 5, pp. 1, Ingenta.   
  32. Solution of the numerical differentiation problem. (Russian)   
    Babenko, L. V.   
    Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 1998, no. 1, 149--153, MathSciNet.  
  33. On the numerical differentiation.
    Lupacs, Alexandru; Mache, Detlef H.   
    Rev. Anal. Numér.  Théor. Approx. 26 (1997), no. 1-2, 109--115, MathSciNet.  
  34. Estimates of the remainders in numerical differentiation for Hermite type nodes.   
    Mitrea, Alexandru I.   
    Automat. Comput. Appl. Math. 6 (1997), no. 1, 16--19, MathSciNet.  
  35. On the convergence of a class of numerical differentiation formulas.   
    Mitrea, Alexandru I.   
    Rev. Anal. Numér. Théor. Approx. 26 (1997), no. 1-2, 125--129, MathSciNet.  
  36. The unbounded superdense divergence of numerical differentiation for extreme odd Chebyshev nodes.   
    Mitrea, A. I.   
    Bul. Stiint. Univ. Politeh. Timis. Ser. Mat. Fiz. 42(56) (1997), no. 2, 30--33, MathSciNet.  
  37. Efficient derivative codes through automatic differentiation and interface contraction: an application in biostatistics.    
    Hovland, P.; Bischof, C.; Spiegelman, D.; Casella, M.   
    SIAM J. Sci. Comput. 18 (1997), no. 4, 1056--1066, MathSciNet.  
  38. Extended backward differentiation methods in the numerical solution of neutral Volterra integro-differential equations.
    Makroglou, A.
    Nonlinear analysis, 1997, vol. 30, no. 3, pp. 1515, Ingenta.   
  39. Numerical Differentiation of Tracking Data of Human Motion: The Virtual Accelerometer.
    Bortolami, S. B.; Riley, P. O.; Krebs, D. E.
    Transactions of the asme. journal of dynamic sy, 1997, vol. 119, no. 2, pp. 355, Ingenta.   
  40. An automatic differentiation technique for sensitivity analysis of numerical advection schemes in air quality models.
    Hwang, D.; Byun, D.W.; Odman, M.T.
    Atmospheric environment., 1997, vol. 31, no. 6, pp. 879, Ingenta.   
  41. Investigation of difference schemes with an approximation of the first derivative by a central difference relation. (Russian)    
    Andreev, V. B.; Kopteva, N. V.    
    Zh. Vychisl. Mat. i Mat. Fiz. 36 (1996), no. 8, 101--117; translation in Comput. Math. Math. Phys. 36 (1996), no. 8, 1065--1078 (1997), MathSciNet.  
  42. High-order stiff ODE solvers via automatic differentiation and rational prediction.   
    Corliss, G. F.; Griewank, A.; Henneberger, P.; Kirlinger, G.; Potra, F. A.; Stetter, H. J.  
    Numerical analysis and its applications (Rousse, 1996), 114--125, Lecture Notes in Comput. Sci., 1196, Springer, Berlin, 1997, MathSciNet.  
  43. A new approach to numerical differentiation and integration.   
    Qu, R.   
    Math. Comput. Modelling 24 (1996), no. 10, 55--68, MathSciNet.  
  44. A universal algorithm for numerical differentiation. (Russian)   
    Guseuinov, Mail Amiroglu  
    Mat. Model. 8 (1996), no. 3, 49--50, MathSciNet.  
  45. Automatic differentiation: the key idea and an illustrative example.    
    Fischer, Herbert   
    Applied mathematics and parallel computing, 121--139, Physica, Heidelberg, 1996, MathSciNet.  
  46. Jet space as the geometric arena of automatic differentiation.   
    Pusch, Gordon D.   
    Computational differentiation (Santa Fe, NM, 1996), 53--62, SIAM, Philadelphia, PA, 1996, MathSciNet.  
  47. An introduction to automatic differentiation.    
    Rall, Louis B.; Corliss, George F.   
    Computational differentiation (Santa Fe, NM, 1996), 1--18, SIAM, Philadelphia, PA, 1996, MathSciNet.  
  48. A parallel implementation of automatic differentiation for partially separable functions using PVM.   
    Conforti, D.; De Luca, L.; Grandinetti, L.; Musmanno, R.   
    Parallel Comput. 22 (1996), no. 5, 643--656, MathSciNet.  
  49. Roles of automatic differentiation in nonlinear analysis and high-quality computation.   
    Iri, Masao    
    Proceedings of the Second World Congress of Nonlinear Analysts, Part 7 (Athens, 1996). Nonlinear Anal. 30 (1997), no. 7, 4317--4328, MathSciNet.  
  50. Global optimization using automatic differentiation: application to quantum chemistry. Shape optimization and scientific computations (Warsaw, 1994).   
    Masmoudi, Mohamed; Massat, Christine; Poteau, Romuald   
    Appl. Math. Comput. Sci. 6 (1996), no. 2, 263--275, MathSciNet.  
  51. Numerical Differentiation and Parameter Estimation in Higher-Order Linear Stochastic Systems.
    Duncan, T. E.; Mandl, P.; Pasik-Duncan, B.
    Ieee transactions on automatic control, 1996, vol. 41, no. 4, pp. 522, Ingenta.   
  52. Numerical Differentiation in Magnetic Field Postprocessing.
    Omeragic, D.; Silvester, P.P.
    International journal of numerical modelling, 1996, vol. 9, no. 1/2, pp. 99, Ingenta.   
  53. Surprising Results Using Calculators for Derivatives  
    Goetz, Albert; Kahan, Jeremy  
    Mathematics Teacher v88 n1 p30-33 Jan 1995
  54. A variational method for numerical differentiation.   
    Knowles, Ian; Wallace, Robert   
    Numer. Math. 70 (1995), no. 1, 91--110, MathSciNet.  
  55. A new smoothing method for obtaining the electron energy distribution function in plasmas by the numerical differentiation of the I-V probe characteristic.
    Palop, J.I. Fernandez; Ballesteros, J.; Hernandez, M.A.
    Review of scientific instruments, 1995, vol. 66, no. 9, pp. 4625, Ingenta.   
  56. Extrapolation to the Limit for Numerical Fractional Differentiation.
    Tuan, Vu Kim; Gorenflo, R.
    Zeitschrift fur angewandte mathematik und mechanik, 1995, vol. 75, no. 8, pp. 646, Ingenta.   
  57. On the numerical differentiation for an extended node matrix of Laguerre type.   
    Mitrea, Alexandru I.   
    Seminar on Mathematical Analysis (Cluj-Napoca, 1993--1994), 15--18, Preprint, 94-7, "Babes-Bolyai" Univ., Cluj-Napoca, 1994, MathSciNet.  
  58. The correct solution of the problem of the numerical differentiation of functions of one or several variables.
    Osipov, I.L.
    Computational mathematics and mathematical physics, 1994, vol. 34, no. 12, pp. 1617, Ingenta.   
  59. Shape design sensitivity analysis of eigenvalues using "exact" numerical differentiation of finite element matrices.
    Lund, E.; Olhoff, N.
    Structural optimization., 1994, vol. 8, no. 1, pp. 52, Ingenta.   
  60. Interpolation and Numerical Differentiation in Civil Engineering Problems.
    Fenton, J.D.
    Transactions of the Institution of Engineers, Australia. Civil engineering, 1994, vol. 36, no.
    4, pp. 331, Ingenta.   
  61. Extended Backward Differentiation Formulae in the Numerical Solution of General Volterra Integro-Differential Equations.
    Makroglou, A.
    Computing, 1993, vol. 51, no. 1, pp. 61, Ingenta.   
  62. Numerical Differentiation of the Formation Function and the Choice of a Chemical Equilibrium Model.
    Povar, I.G.
    Russian journal of inorganic chemistry, 1993, vol. 38, no. 11, pp. 1787, Ingenta.   
  63. Numerical differentiation in movement analysis: how to standardise the evaluation of techniques.
    Corradini, M.L.; Fioretti, S.; Leo, T.
    Medical & biological engineering & computing, 1993, vol. 31, no. 2, pp. 187, Ingenta.   
  64. On the numerical differentiation for Laguerre nodes.   
    Mitrea, Alexandru-I.   
    Seminar on Mathematical Analysis (Cluj-Napoca, 1992--1993), 63--68, Preprint, 93-7, "Babec s-Bolyai" Univ., Cluj-Napoca, 1993, MathSciNet.  
  65. Automatic differentiation and applications.    
    Fischer, Hans Christoph   
    Scientific computing with automatic result verification,  105--142, Math. Sci. Engrg., 189, Academic Press, Boston, MA, 1993, MathSciNet.  
  66. Central Difference Formula in Numerical Analysis  
    Tilak de Alwis  
    PRIMUS, Vol. II, No. 2, (1992), pp. 165-172.  
  67. Lagrange interpolation on a lattice: bounding derivatives by divided differences.    
    Kunkle, Thomas    
    J. Approx. Theory 71 (1992), no. 1, 94--103, MathSciNet.  
  68. On some numerical differentiation formulas.   
    Mitrea, A.-I.   
    Proceedings of the Fourth Symposium of Mathematics and its Applications (Timisoara, 1991), 116--120, Mirton, Timi\c soara, 1992, MathSciNet.  
  69. The Numerical Differentiation of Probe Characteristic.
    Trunec, D.
    Contributions to plasma physics, 1992, vol. 32, no. 5, pp. 523, Ingenta.   
  70. Numerical Calculation of Derivatives  
    William H. Press  and  Saul A. Teukolsky  
    Computers in Physics, (Jan-Feb 1991), pp 68-69.    
  71. On the convergence of numerical differentiation for Hermite nodes.   
    Mitrea, Alexandru-I.   
    Seminar on Mathematical Analysis, 65--70, Preprint, 91-7, "Babec s-Bolyai" Univ., Cluj-Napoca, 1991, MathSciNet.  
  72. Fréchet derivative as a limit of divided differences.    
    Balázs, M.; Goldner, G.    
    Seminar on Mathematical Analysis, 115--120, Preprint, 91-7, "Babes-Bolyai" Univ., Cluj-Napoca, 1991, MathSciNet.  
  73. Use of automatic differentiation for calculating Hessians and Newton steps.   
    Dixon, Laurence C. W.   
    Automatic differentiation of algorithms (Breckenridge, CO, 1991), 114--125, SIAM, Philadelphia, PA, 1991, MathSciNet.  
  74. History of automatic differentiation and rounding error estimation.   
    Iri, Masao   
    Automatic differentiation of algorithms (Breckenridge, CO, 1991), 3--16, SIAM, Philadelphia, PA, 1991, MathSciNet.  
  75. Automatic differentiation from an oceanographer's perspective.    
    Thacker, William Carlisle   
    Automatic differentiation of algorithms (Breckenridge, CO, 1991), 191--201, SIAM, Philadelphia, PA, 1991, MathSciNet.  
  76. Neural networks, backpropagation, and automatic differentiation.    
    Saarinen, Sirpa; Bramley, Randall B.; Cybenko, George   
    Automatic differentiation of algorithms (Breckenridge, CO, 1991), 31--42, SIAM, Philadelphia, PA, 1991, MathSciNet.  
  77. Numerical differentiation of analytic functions.
    McGregor, Malcolm T.
    Publikacije Elektrotehnickog fakulteta. Serija Matematika, 1991, vol. 2, pp. 11, Ingenta.   
  78. Numerical differentiation of analytic functions using quadratures on the semicircle.
    Calio, F.; Fronti, M.; Milovanovic, G.V.
    Computers & mathematics with applications, 1991, vol. 22, no. 10, pp. 99, Ingenta.   
  79. A discussion of simultaneous approximation of derivatives by Lagrange interpolation.   
    Balázs, K.; Kilgore, T.   
    Numer. Funct. Anal. Optim. 11 (1990), no. 3-4, 225--237, MathSciNet.  
  80. Numerical differentiation of experimental data using the Fourier transform.
    Kavkyanov, S.I.; Strepetova, S.V.
    Atmospheric optics, 1990, vol. 3, no. 11, pp. 1102, Ingenta.   
  81. Contribution toward the Solution of the Problem of Numerical Differentiation by the Method of Statistical Regularization.
    Ustinov, E.A.
    Cosmic research, 1990, vol. 28, no. 4, pp. 466, Ingenta.   
  82. Discrete stability analysis of the molification method for numerical differentiation.
    Murio, D.A.; Guo, L.
    Computers & mathematics with applications, 1990, vol. 19, no. 6, pp. 15, Ingenta.   
  83. Systolic estimation of derivatives using Richardson-Romberg's extrapolation method for central-divided differences.   
    Cruceanu, M.    
    Bul. Inst. Politehn. Iasi Sect. I 35(39) (1989), no. 1-2, 69--74, MathSciNet.  
  84. Fast automatic differentiation on a computer. (Russian)   
    Aui da-zade, K. R.; Evtushenko, Yu. G.   
    Mat. Model. 1 (1989), no. 1, 120--131, MathSciNet.  
  85. On index commutativity in numerical differentiation.
    Bazhenov, V.G.; Chekmarev, D.T.
    U.S.S.R. computational mathematics and mathematical physics, 1989, vol. 29, no. 3, pp. 13, Ingenta.   
  86. On numerical differentiation problem.
    Egorov, Yu.V.; Kondrat'ev, V.A.
    Moscow University mathematics bulletin, 1989, vol. 44, no. 3, pp. 85, Ingenta.   
  87. Numerical Differentiation for Use in Integrating Unified Constitutive Equations.
    Henshall, G. A.; Tanaka, T. G.; Miller, A. K.; Lowe, T. C.
    International journal for numerical methods in e, 1989, vol. 28, no. 5, pp. 1115, Ingenta.   
  88. Numerical Differentiation of Implicitly Defined Space Curves.
    Mackens, W.
    Computing, 1989, vol. 41, no. 3, pp. 237, Ingenta.   
  89. On automatic differentiation.   
    Griewank, Andreas  
    Mathematical programming (Tokyo, 1988), 83--107, Math. Appl. (Japanese Ser.), 6, KTK Scientific, Tokyo, 1989, MathSciNet.  
  90. Noncentral Difference Quotients and the Derivative (in The Teaching of Mathematics)  
    P. P. B. Eggermont  
    American Mathematical Monthly, Vol. 95, No. 6. (Jun. - Jul., 1988), pp. 551-553, Jstor.  
  91. On the convergence of some numerical differentiation formulas.   
    Mitrea, Alexandru-I.   
    Seminar on Mathematical Analysis (Cluj-Napoca, 1987--1988), 151--166, Preprint, 88-7, Univ. "Babec s-Bolyai", Cluj-Napoca, 1988, MathSciNet.  
  92. The nth Derivative as a Limit (in Notes)  
    J. B. Wilker  
    American Mathematical Monthly, Vol. 94, No. 4. (Apr., 1987), pp. 354-356, Jstor.  
  93. Numerical differentiation by high order interpolation.   
    Hoffman, Peter; Reddy, K. C.   
    SIAM J. Sci. Statist. Comput. 8 (1987), no. 6, 979--987, MathSciNet.  
  94. Global optimization using automatic differentiation and interval iteration.   
    Rall, L. B.   
    Transactions of the fourth Army conference on applied mathematics and computing (Ithaca, N.Y., 1986), 881--900, ARO Rep., 87-1, U.S. Army Res. Office, Research Triangle Park, NC, 1987, MathSciNet.  
  95. On a Numerical Differentiation  
    Dragoslav Herceg, Ljiljana Cvetkovic  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 3. (Jun., 1986), pp. 686-691, Jstor.  
  96. Hybrid predictor-corrector methods based on numerical differentiation.   
    Rao, C. Prabhakara   
    J. Math. Phys. Sci. 20 (1986), no. 1, 43--53, MathSciNet.  
  97. Divided difference tables with derivatives for interpolation and numerical integration.    
    Goodyear, William H.    
    J. Astronaut. Sci. 34 (1986), no. 3, 287--314, MathSciNet.  
  98. On the condition number of Lagrangian numerical differentiation.   
    Miel, George; Mooney, Rose   
    Appl. Math. Comput. 16 (1985), no. 3, 241--252, MathSciNet.  
  99. Finite difference methods for the numerical differentiation of nonexact data.   
    Anderssen, R. S.; de Hoog, F. R.   
    Computing 33 (1984), no. 3-4, 259--267, MathSciNet.  
  100. Interpolation und numerische Differentiation. (German)   
    Forst, Wilhelm   
    [Interpolation and numerical differentiation]
    J. Approx. Theory 39 (1983), no. 2, 118--131, MathSciNet.  
  101. Numerical differentiation and integration on the basis of interpolation parabolic splines. (Russian)   
    Kvasov, B. I.   
    Chisl. Metody Mekh. Sploshn. Sredy 14 (1983), no. 2, 68--80, MathSciNet.  
  102. The relation between higher differences and higher derivatives. (Chinese)    
    Zhou, Hui Shan    
    Qufu Shiyuan Xuebao 1983, no. 1, 39--43, MathSciNet.  
  103. Simplification of remainder terms of formulas of numerical differentiation. (Russian)  
    Volkov, V. E.   
    Zh. Vychisl. Mat. i Mat. Fiz. 22 (1982), no. 2, 465--467, 496, MathSciNet.  
  104. The numerical differentiation of discrete functions using polynomial interpolation methods.   
    Hyman, James M.; Larrouturou, Bernard   
    Numerical grid generation (Nashville, Tenn., 1982). Appl. Math. Comput. 10/11 (1982), 487--506, MathSciNet.  
  105. Second Derivative Extended Backward Differentiation Formulas for the Numerical Integration of Stiff Systems (in SIGNUM Meeting on Numerical Ordinary Differential Equations)  
    J. R. Cash  
    SIAM Journal on Numerical Analysis, Vol. 18, No. 1. (Feb., 1981), pp. 21-36, Jstor.  
  106. On a Numerical Differentiation  
    Dragoslav Herceg, Ljiljana Cvetkovic  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 3. (Jun., 1986), pp. 686-691, Jstor.  
  107. Numerical Solution of Nonlinear Differential Equations with Algebraic Constraints I: Convergence Results for Backward Differentiation Formulas  
    Per Lotstedt, Linda Petzold  
    Mathematics of Computation, Vol. 46, No. 174. (Apr., 1986), pp. 491-516, Jstor.  
  108. Optimal Numerical Differentiation Using Three Function Evaluations  
    J. Marshall Ash, Roger L. Jones  
    Mathematics of Computation, Vol. 37, No. 155. (Jul., 1981), pp. 159-167, Jstor.  
  109. On remainders of numerical differentiation formulas. II. (Chinese)   
    Wang, Xing Hua   
    Numer. Math. J. Chinese Univ. 3 (1981), no. 3, 283--285, MathSciNet.  
  110. Finite difference approximation for ordinary derivatives.    
    Lau, P. C. M.    
    Internat. J. Numer. Methods Engrg. 17 (1981), no. 5, 663--678, MathSciNet.  
  111. Convergence of numerical differentiation.   
    Lorentz, R. A.  
    J. Approx. Theory 30 (1980), no. 1, 59--70, MathSciNet.  
  112. New estimates of errors of quadrature formulae, formulae of numerical differentiation and interpolation.   
    Ivanov, Kamen G.   
    Anal. Math. 6 (1980), no. 4, 281--303, MathSciNet.  
  113. On the evaluation of finite difference derivatives using interpolated data  
    Spiegel, Stanley L.  
    Internat. J. Math. Ed. Sci. Tech. 11 (1980), no. 3, 391--399, MathSciNet.  
  114. Taylor Polynomials and Difference Quotients (in Mathematical Notes)  
    Richard J. Bagby  
    American Mathematical Monthly, Vol. 86, No. 8. (Oct., 1979), pp. 681-684, Jstor.  
  115. Adaptive Numerical Differentiation  
    R. S. Stepleman, N. D. Winarsky  
    Mathematics of Computation, Vol. 33, No. 148. (Oct., 1979), pp. 1257-1264, Jstor.  
  116. The remainder terms of a formula for numerical differentiation. (Chinese)   
    Wang, Xing Hua   
    Kexue Tongbao 24 (1979), no. 19, 869--872, MathSciNet.  
  117. Derivatives on the Hand-Held Calculator  
    Morgan, Raymond V.; Warnock, Tony T.
    Mathematics Teacher v71 n6 p532-37 Sep 1978, Sep78
  118. Numerical Differentiation for Calculus Students (in Classroom Notes)  
    David A. Smith  
    American Mathematical Monthly, Vol. 82, No. 3. (Mar., 1975), pp. 284-287, Jstor.  
  119. Bounds for Difference Quotients and Derivates (in Classroom Notes)  
    Roger Chalkley  
    American Mathematical Monthly, Vol. 82, No. 3. (Mar., 1975), pp. 277-279, Jstor.  
  120. Optimally Stable Lagrangian Numerical Differentiation  
    T. J. Rivlin  
    SIAM Journal on Numerical Analysis, Vol. 12, No. 5. (Oct., 1975), pp. 712-725, Jstor.  
  121. The selection of interpolation points in numerical differentiation.   
    Oliver, J.; Ruffhead, A.   
    Nordisk Tidskr. Informationsbehandling (BIT) 15 (1975), no. 3, 283--295, MathSciNet.  
  122. On the divided differences and Fréchet derivatives.    
    Goldner, G.    
    Rev. Anal. Numér. Théorie Approximation 3 (1974), no. 1, 33--36, MathSciNet.  
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    Anderssen, R. S.; Bloomfield, P.   
    Numer. Math. 22 (1973/74), 157--182, MathSciNet.  
  124. An error analysis for numerical differentiation.   
    Johnson, L. W.; Riess, R. D.   
    J. Inst. Math. Appl. 11 (1973), 115--120, MathSciNet.  
  125. Minimal Error Constant Numerical Differentiation (N.D.) Formulas  
    A. Pelios, R. W. Klopfenstein  
    Mathematics of Computation, Vol. 26, No. 118. (Apr., 1972), pp. 467-475, Jstor.  
  126. Numerical differentiation by extrapolation.   
    Chanda, Manas; Sen, Syamal Kumar   
    J. Indian Inst. Sci. 53 (1971), 51--55, MathSciNet.  
  127. Numerical Differentiation and Regularization  
    Jane Cullum  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 254-265, Jstor.  
  128. Efficient Algorithms for Polynomial Interpolation and Numerical Differentiation  
    Fred T. Krogh  
    Mathematics of Computation, Vol. 24, No. 109. (Jan., 1970), pp. 185-190, Jstor.  
  129. Numerical Differentiation and the Solution of Multidimensional Vandermonde Systems  
    G. Galimberti, V. Pereyra  
    Mathematics of Computation, Vol. 24, No. 110. (Apr., 1970), pp. 357-364, Jstor.  
  130. Symmetric differences and derivatives.    
    Meir, A.; Sharma, A.    
    Nederl. Akad. Wetensch. Proc. Ser. A 71=Indag. Math. 30 1968 353--360, MathSciNet.  
  131. The First Symmetric Derivative (in Classroom Notes)  
    C. E. Aull  
    American Mathematical Monthly, Vol. 74, No. 6. (Jun. - Jul., 1967), pp. 708-711, Jstor.  
  132. A modification of Davidon's minimization method to accept difference approximations of derivatives.    
    Stewart, G. W., III    
    J. Assoc. Comput. Mach. 14 1967 72--83, MathSciNet.  
  133. Numerical Differentiation of Analytic Functions  
    J. N. Lyness, C. B. Moler  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 2. (Jun., 1967), pp. 202-210, Jstor.  
  134. Difference Quotients and the Teaching of the Derivative  
    Zlot, William Leonard  
    Mathematics Magazine 36 (1963) 63-64.
  135. Numerical Integration and Differentiation of Functions of Several Independent Variables by an Iterative Procedure  
    Henry C. Thacher, Jr.  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 3. (Sep., 1963), pp. 614-622, Jstor.  
  136. An error formula for numerical differentiation.   
    Kranzer, H. C.
    Numer. Math. 5 1963 439--442, MathSciNet.  
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    Salzer, Herbert E.    
    J. Math. and Phys. 42 1963 162--165, MathSciNet.  
  138. Truncation error in interpolation and numerical differentiation.   
    Chakravarti, P. C.  
    Numer. Math. 3 1961 279--284, MathSciNet.  
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    Hildebrand, F. B.   
    J. Math. and Phys. 39 1960/1961 151--154, MathSciNet.  
  140. Optimal points for numerical differentiation.   
    Salzer, Herbert E.   
    Numer. Math. 2 1960 214--227, MathSciNet.  
  141. Extension of Lindow's Tables for Numerical Differentiation Using Newton-Stirling and Newton-Bessel Differences
    Herbert E. Salzer, Genevieve M. Kimbro  
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    A. Spitzbart, N. Macon  
    American Mathematical Monthly, Vol. 64, No. 10. (Dec., 1957), pp. 721-723, Jstor.  
  143. A Method for Deriving Numerical Differentiation Formulas  
    R. T. Gregory  
    American Mathematical Monthly, Vol. 64, No. 2. (Feb., 1957), pp. 79-82, Jstor.  
  144. On divided differences in terms of derivatives.    
    Simonsen, W.    
    Skand. Aktuarietidskr 40 1957 26--45, MathSciNet.  
  145. Table of coefficients for obtaining the second derivative without differences.   
    Salzer, Herbert E.; Roberson, Peggy T.    
    Convair-Astronautics, San Diego, Calif., 1957, MathSciNet.  
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    Corominas Vigneaux, Ernesto    
    Rev. Acad. Ci. Madrid 49 (1955), 115--212, MathSciNet.  
  147. Mach Rings Verified by Numerical Differentiation  
    Robert W. Burnham, J. Edward Jackson  
    Science, New Series, Vol. 122, No. 3177. (Nov. 18, 1955), pp. 951-953, Jstor.  
  148. On the Remainder in Formulas of Numerical Interpolation, Differentiation and Quadrature (in Classroom Notes)  
    Harry Goheen  
    American Mathematical Monthly, Vol. 61, No. 1. (Jan., 1954), pp. 44-46, Jstor.  
  149. Computing derivatives of least square polynomials using differences.    
    Trimble, George R., Jr.
    Tech. Note No. 898, Ballistic Research Laboratories, Aberdeen Proving Ground, Md., (1954), MathSciNet.  
  150. Derivatives and finite differences.    
    Kloosterman, H. D.    
    Duke Math. J. 17, (1950). 169--186, MathSciNet.  
  151. Table of coefficients for obtaining the first derivative without differences.    
    Salzer, Herbert E.    
    National Bureau of Standards. Appl. Math. Ser., 1948, (1948). no. 2, 20 pp., MathSciNet.  
  152. Table of coefficients for differences in terms of the derivatives.    
    Salzer, Herbert E.    
    J. Math. Phys. Mass. Inst. Tech. 23, (1944). 210--212, MathSciNet.  
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    Salzer, Herbert E.    
    J. Math. Phys. Mass. Inst. Tech. 22, (1943). 115--135, MathSciNet.  
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    Bickley, W. G.  
    Math. Gaz. 25, (1941). 19--27, MathSciNet.  
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    John W. Cell  
    American Mathematical Monthly, Vol. 46, No. 2. (Feb., 1939), pp. 87-92, Jstor.
  156. Derivatives, Difference Quotients and Taylor's Formula II  
    Hassler Whitney  
    The Annals of Mathematics, 2nd Ser., Vol. 35, No. 3. (Jul., 1934), pp. 476-481, Jstor.
  157. Difference Quotients  
    J. P. Ballantine  
    American Mathematical Monthly, Vol. 26, No. 2. (Feb., 1919), pp. 53-59, Jstor.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004