Bibliography for Numerical Differentiation

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  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. 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.  
  4. 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.  
  5. On stable numerical differentiation
    Ramm, A. G.; Smirnova, A. B.
    Mathematics of Computation, 2001, vol. 70, no. 235, pp. 1131-1154, Ingenta.  
  6. Inverse Problems Light: Numerical Differentiation  
    Hanke, M.; Scherzer, O.  
    American Mathematical Monthly, 2001, vol. 108, no. 6, pp. 512-521, Ingenta.  
  7. New finite difference formulas for numerical differentiation.  
    Khan, Ishtiaq Rasool; Ohba, Ryoji   
    J. Comput. Appl. Math. 126 (2000), no. 1-2, 269--276, MathSciNet.  
  8. An introduction to automatic differentiation.    
    Verma, Arun    
    Current Sci. 78 (2000), no. 7, 804--807, MathSciNet.  
  9. A new approach to numerical differentiation and integration.   
    Qu, R.   
    Math. Comput. Modelling 24 (1996), no. 10, 55--68, MathSciNet.  
  10. Surprising Results Using Calculators for Derivatives  
    Goetz, Albert; Kahan, Jeremy  
    Mathematics Teacher v88 n1 p30-33 Jan 1995
  11. Central Difference Formula in Numerical Analysis  
    Tilak de Alwis  
    PRIMUS, Vol. II, No. 2, (1992), pp. 165-172.  
  12. Lagrange interpolation on a lattice: bounding derivatives by divided differences.    
    Kunkle, Thomas    
    J. Approx. Theory 71 (1992), no. 1, 94--103, MathSciNet.  
  13. Numerical Calculation of Derivatives  
    William H. Press  and  Saul A. Teukolsky  
    Computers in Physics, (Jan-Feb 1991), pp 68-69.    
  14. 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.  
  15. The nth Derivative as a Limit (in Notes)  
    J. B. Wilker  
    American Mathematical Monthly, Vol. 94, No. 4. (Apr., 1987), pp. 354-356, Jstor.  
  16. Numerical differentiation by high order interpolation.   
    Hoffman, Peter; Reddy, K. C.   
    SIAM J. Sci. Statist. Comput. 8 (1987), no. 6, 979--987, MathSciNet.  
  17. On a Numerical Differentiation  
    Dragoslav Herceg, Ljiljana Cvetkovic  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 3. (Jun., 1986), pp. 686-691, Jstor.  
  18. Divided difference tables with derivatives for interpolation and numerical integration.    
    Goodyear, William H.    
    J. Astronaut. Sci. 34 (1986), no. 3, 287--314, MathSciNet.  
  19. 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.  
  20. On a Numerical Differentiation  
    Dragoslav Herceg, Ljiljana Cvetkovic  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 3. (Jun., 1986), pp. 686-691, Jstor.  
  21. 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.  
  22. 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.  
  23. 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.  
  24. Taylor Polynomials and Difference Quotients (in Mathematical Notes)  
    Richard J. Bagby  
    American Mathematical Monthly, Vol. 86, No. 8. (Oct., 1979), pp. 681-684, Jstor.  
  25. Adaptive Numerical Differentiation  
    R. S. Stepleman, N. D. Winarsky  
    Mathematics of Computation, Vol. 33, No. 148. (Oct., 1979), pp. 1257-1264, Jstor.  
  26. Derivatives on the Hand-Held Calculator  
    Morgan, Raymond V.; Warnock, Tony T.
    Mathematics Teacher v71 n6 p532-37 Sep 1978, Sep78
  27. Numerical Differentiation for Calculus Students (in Classroom Notes)  
    David A. Smith  
    American Mathematical Monthly, Vol. 82, No. 3. (Mar., 1975), pp. 284-287, Jstor.  
  28. Bounds for Difference Quotients and Derivates (in Classroom Notes)  
    Roger Chalkley  
    American Mathematical Monthly, Vol. 82, No. 3. (Mar., 1975), pp. 277-279, Jstor.  
  29. Optimally Stable Lagrangian Numerical Differentiation  
    T. J. Rivlin  
    SIAM Journal on Numerical Analysis, Vol. 12, No. 5. (Oct., 1975), pp. 712-725, Jstor.  
  30. 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.  
  31. Numerical Differentiation and Regularization  
    Jane Cullum  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 254-265, Jstor.  
  32. Efficient Algorithms for Polynomial Interpolation and Numerical Differentiation  
    Fred T. Krogh  
    Mathematics of Computation, Vol. 24, No. 109. (Jan., 1970), pp. 185-190, Jstor.  
  33. 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.  
  34. The First Symmetric Derivative (in Classroom Notes)  
    C. E. Aull  
    American Mathematical Monthly, Vol. 74, No. 6. (Jun. - Jul., 1967), pp. 708-711, Jstor.  
  35. 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.  
  36. Difference Quotients and the Teaching of the Derivative  
    Zlot, William Leonard  
    Mathematics Magazine 36 (1963) 63-64.
  37. 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.  
  38. Optimal points for numerical differentiation.   
    Salzer, Herbert E.   
    Numer. Math. 2 1960 214--227, MathSciNet.  
  39. Extension of Lindow's Tables for Numerical Differentiation Using Newton-Stirling and Newton-Bessel Differences
    Herbert E. Salzer, Genevieve M. Kimbro  
    Mathematical Tables and Other Aids to Computation, Vol. 12, No. 62. (Apr., 1958), pp. 133-140, Jstor.  
  40. Numerical Differentiation Formulas  
    A. Spitzbart, N. Macon  
    American Mathematical Monthly, Vol. 64, No. 10. (Dec., 1957), pp. 721-723, Jstor.  
  41. A Method for Deriving Numerical Differentiation Formulas  
    R. T. Gregory  
    American Mathematical Monthly, Vol. 64, No. 2. (Feb., 1957), pp. 79-82, Jstor.  
  42. Table of coefficients for obtaining the second derivative without differences.   
    Salzer, Herbert E.; Roberson, Peggy T.    
    Convair-Astronautics, San Diego, Calif., 1957, MathSciNet.  
  43. 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.  
  44. 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.  
  45. Formulae for numerical differentiation  
    Bickley, W. G.  
    Math. Gaz. 25, (1941). 19--27, MathSciNet.  
  46. An Accurate Method for Obtaining the Derivative Function from Observational Data  
    John W. Cell  
    American Mathematical Monthly, Vol. 46, No. 2. (Feb., 1939), pp. 87-92, Jstor.
  47. 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.
  48. Difference Quotients  
    J. P. Ballantine  
    American Mathematical Monthly, Vol. 26, No. 2. (Feb., 1919), pp. 53-59, Jstor.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004