[1] |
Anderssen, R. S.; Bloomfield, P.: Numerical differentiation procedures for non-exact data. Numer. math. 22, 157-182 (1973/74) |

[2] |
Burden, R. L.; Faires, J. D.: Numerical analysis. (2001) · Zbl 0671.65001 |

[3] |
Chapra, S. C.; Canale, R. P.: Numerical methods for engineers. (1998) |

[4] |
Collatz, L.: The numerical treatment of differential equations. (1966) · Zbl 0173.17702 |

[5] |
Corliss, G.; Faure, C.; Griewank, A.; Hascoet, L.; Naumann, U.: Automatic differentiation of algorithms --- from simulation to optimization. (2002) · Zbl 0983.68001 |

[6] |
Cullum, J.: Numerical differentiation and regularization. SIAM J. Numer. anal. 8, No. 2, 254-265 (1971) · Zbl 0224.65005 |

[7] |
Dahlquist, G.; Bjorck, A.: Numerical methods. (1974) |

[8] |
Dokken, T.; Lyche, T.: A divided difference formula for the error in Hermite interpolation. Bit 19, 539-540 (1979) · Zbl 0428.41002 |

[9] |
Forst, W.: Interpolation und numerische differentiation. J. approx. Theory 39, No. 2, 118-131 (1983) · Zbl 0525.41008 |

[10] |
Gerald, C. F.; Wheatley, P. O.: Applied numerical analysis. (1989) · Zbl 0684.65002 |

[11] |
Grabar, L. P.: Numerical differentiation by means of Chebyshev polynomials orthonormalized on a system of equidistant points. Zh. vychisl, mat. I mat. Fiz. 7, No. 6, 1375-1379 (1967) · Zbl 0171.37301 |

[12] |
Griewank, A.: Evaluating derivatives, principles and techniques of algorithmic differentiation, number 19 in frontiers in applied mathematics. (2000) · Zbl 0958.65028 |

[13] |
Griewank, A.; Corliss, F.: Automatic differentiation of algorithms --- theory, implementation and application. (1991) · Zbl 0747.00030 |

[14] |
Hamming, R. W.: Numerical methods for scientists and engineers. (1962) · Zbl 0952.65500 |

[15] |
Hanke, M.; Scherzer, O.: Inverse problems light --- numerical differentiation. Amer. math. Monthly 6, 512-522 (2001) · Zbl 1002.65029 |

[16] |
Heath, M. T.: Science computing --- an introductory survey. (1997) |

[17] |
Khan, I. R.; Ohba, R.: Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series. J. comput. Appl. math. 107, 179-193 (1999) · Zbl 0939.65031 |

[18] |
Khan, I. R.; Ohba, R.: Digital differentiators based on Taylor series. IEICE trans. Fund. 82-A, No. 12, 2822-2824 (1999) |

[19] |
Khan, I. R.; Ohba, R.: New finite difference formulas for numerical differentiation. J. comput. Appl. math. 126, 269-276 (2001) · Zbl 0971.65014 |

[20] |
Khan, I. R.; Ohba, R.: Mathematical proof of explicit formulas for TAP-coefficients of Taylor series based FIR digital differentiators. IEICE trans. Fund. 84-A, No. 6, 1581-1584 (2001) |

[21] |
Khan, I. R.; Ohba, R.: Taylor series based finite difference approximations of higher-degree derivatives. J. comput. Appl. math. 154, 115-124 (2003) · Zbl 1018.65032 |

[22] |
Khan, I. R.; Ohba, R.; Hozumi, N.: Mathematical proof of closed form expressions for finite difference approximations based on Taylor series. J. comput. Appl. math. 150, 303-309 (2003) · Zbl 1017.65015 |

[23] |
King, T.; Murio, D.: Numerical differentiation by finite dimensional regularization. IMA J. Numer. anal. 6, 65-85 (1986) · Zbl 0584.65008 |

[24] |
Knowles, I.; Wallace, R.: A variational method for numerical differentiation. Numer. math. 70, 91-110 (1995) · Zbl 0818.65013 |

[25] |
Kreyzig, E.: Advanced engineering mathematics. (1994) |

[26] |
Krishnamurti, T. N.; Bounoua, L.: An introduction to numerical weather prediction technique techniques. (1995) |

[27] |
Kvasov, B. I.: Numerical differentiation and integration on the basis of interpolation parabolic splines. Chisl. metody mekh. Sploshn. sredy 14, No. 2, 68-80 (1983) |

[28] |
Mathews, J. H.; Fink, K. D.: Numerical methods using Matlab. (1999) |

[29] |
Murio, D. A.: The mollification method and the numerical solution of ill-posed problems. (1993) |

[30] |
Rail, L. B.: Automatic differentiation --- techniques and applications. (1981) |

[31] |
Ramm, A. G.: On numerical differentiation. Mathem. izvestija vuzov 11, 131-135 (1968) · Zbl 0187.10504 |

[32] |
Ramm, A. G.: Stable solutions of some ill-posed problems. Math. meth. Appl. sci. 3, 336-363 (1981) · Zbl 0469.65034 |

[33] |
Silvester, P.: Numerical formation of finite-difference operators. IEEE trans. Microwave theory technol. 18, No. 10, 740-743 (1970) |

[34] |
Tikhonov, A. N.; Arsenin, V. Y.: Solutions of ill-posed problems. (1977) · Zbl 0354.65028 |

[35] |
Vasin, V. V.: Regularization of the problem of numerical differentiation. Matem. zap. Uralâ€™skii univ. 7, No. 2, 29-33 (1969) |

[36] |
Vershinin, V. V.; Pavlov, N. N.: Approximation of derivatives by smoothing splines. Vychisl. sistemy 98, 83-91 (1983) · Zbl 0566.41028 |

[37] |
Wahba, G.: Spline models for observational data. (1990) · Zbl 0813.62001 |