Optimal Recovery of the Derivative of the Function from its Inaccurately Given Other Orders of Derivatives and the Function Itself

		ISSN 1683-3414 (Print) • ISSN 1814-0807 (Online)

Home Editorial board Publication ethics Peer review guidelines Current Archive Rules for authors Contacts Address: Markusa st. 22, Vladikavkaz, 362027, RNO-A, Russia Phone: (8672)50-18-06 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.3.5877 Optimal Recovery of the Derivative of the Function from its Inaccurately Given Other Orders of Derivatives and the Function Itself Unuchek S. A. Vladikavkaz Mathematical Journal 2016. Vol. 18. Issue 3. Abstract: The paper deals with the problem of simultaneous recovery of the \(k_1\)-th and \(k_2\)-th order derivatives of a function in the mean square norm from inaccurately given derivatives of \(n_1\)-th and \(n_2\)-th order and the function itself. The solution is given under some conditions on the errors of given derivatives and the function itself. The problem is solved completely for the case \(k_1=k\), \(n_1=2k\), \(k_2=3k\), \(n_2=4k\), \(k\in\mathbb N\). It turns out that in contrast to previously encountered situations in the general case, the error of recovery depends on errors of all three errors of input data. Keywords: optimal method, Fourier transform, extremal problem Language: Russian Download the full text + References Smolyak S. A. On Optimal Recovery of Fuctions and Functionals of them, Candidate dissertation, Moscow State University, 1965. [in Russian] Nikol'skii S. M. Quadrature Formulas, Nauka Publishers, Moscow, 1988. [in Russian] Marchuk A. G., Osipenko K. Y. Best Approximation of Functions Specified with an Error at a Finite Number of Points. Mathematical Notes of the Academy of Sciences of the USSR [Matematicheskie Zametki]. 1975, vol. 17, no 3, pp. 359-368. [in Russian] Magaril-Il'yaev G. G., Osipenko K. Y. Optimal Recovery of Functions and their Derivatives from Fourier Coefficients Prescribed with an Error. Matematicheskiy Sbornik [Sbornik: Mathematics]. 2002, vol. 193, no 3, pp. 79-100. [in Russian] Magaril-Il'yaev G. G., Osipenko K. Y. Optimal Recovery of Functions and their Derivatives from Inaccurate Information about the Spectrum and Inequalities for Derivatives. Functional Analysis and Its Applications [Functionalniy Analis i ego Prilogeniya]. 2003, vol. 37, no. 3, pp. 203-214. [in Russian] Magaril-Il'yaev, G. G., Osipenko, K. Yu. The Hardy-Littlewood-Paley Inequality and the Reconstruction of Derivatives from Inaccurate Data, Dokl. Math., 2011, vol. 83, no. 3, pp. 337-339. ← Contents of issue


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