Method for Integrating Tabular Functions that Considers Errors
Applied and Computational Mathematics
Volume 3, Issue 2, April 2014, Pages: 63-67
Received: May 3, 2014;
Accepted: May 13, 2014;
Published: May 20, 2014
Views 2514 Downloads 140
Vladimir V. Ternovski, Lomonosov State University, Numerical Math and Cyber Departament, Moscow, Russia
Mikhail M. Khapaev, Lomonosov State University, Numerical Math and Cyber Departament, Moscow, Russia
Follow on us
If experimental tables are numerically integrated using quadrature formulas, then the measurement errors of the physical instrument is not taken into account. The result of such numerical integration will be inaccurate because of the accumulation of errors due to the summation of random values, and the residual term of the quadrature formula cannot be calculated using solely classical concepts. The traditional approach consists of applying various smoothing algorithms. In this case, methods are used that are unrelated to the problem of integrating itself, which leads to excessive smoothing of the result. The authors propose a method for numerical integration of inaccurate numerical functions that minimizes the residual term of the quadrature formula for the set of unknown values based on the error confidence intervals by using ill-posed problem algorithms. The high level of effectiveness of this new method, for which it is sufficient to know the error level of the signal, is demonstrated through examples.
Quadrature Formula, Ill-Posed Problem, Tikhonov Regularization
To cite this article
Vladimir V. Ternovski,
Mikhail M. Khapaev,
Method for Integrating Tabular Functions that Considers Errors, Applied and Computational Mathematics.
Vol. 3, No. 2,
2014, pp. 63-67.
A. Tikhonov and V. Arsenin, Solutions of ill-posed problems. Winston, Washington, DC(1977).
A. Bakushinsky and A. Goncharsky, Ill-posed problems: theory and applications. Springer Netherlands (1994).
T. Prvan , Integrating noisy data, Appl.Math.Lett.(1995) Vol. 8, No.6: 83-87.
V.V. Ternovskii and M.M. Khapaev, Reconstruction of periodic function from noisy input data , Doklady Mathematics(2009) Vol.79,No.1:81-82.