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Identification of a source function by B-spline regularization

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Abbreviations

L:

differential operator

u(x), f(x):

measured and unknown functions

p(x), q(x), r(x):

coefficients in the differential equation

Ω:

region of function determination

B nk (x):

k-thbasic spline of order n

ɛs :

error in solution of the linear equation system

ɛI :

interpolation error

ωH(f):

modulus of the discontinuity of f(x) in the interval of length H

h:

measuring interval step

σ:

standard deviation of measurement error

Literature cited

  1. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Irregular Problems [in Russian], Nauka, Moscow (1979).

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  2. Yu. S. Zav'yalov, B. I. Kvasov, and V. L. Miroshnichenko, Spline-Function Methods [in Russian], Nauka, Moscow (1980).

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  3. G. I. Marchuk, Methods of Numerical Mathematics, Springer-Verlag (1975).

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Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 45, No. 5, pp. 818–821, November, 1983.

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Kaminskas, V.A., Sakalauskas, É.I. Identification of a source function by B-spline regularization. Journal of Engineering Physics 45, 1309–1311 (1983). https://doi.org/10.1007/BF01254741

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  • DOI: https://doi.org/10.1007/BF01254741

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