{"title":"Uncontrollable Inaccuracy in Inverse Problems ","authors":"Yu. Menshikov ","volume":104,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":494,"pagesEnd":499,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10002513","abstract":"<p>In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solutions are analyzed. Several methods for removing the influence of uncontrollable inaccuracy have been suggested.&nbsp;<\/p>\r\n","references":"[1] A. Prilepko, D. Orlovsky, \u201cAbout inverse problems for nonsteady\r\nsystems\u201d, Different. Equations and their Applications, Vilnus, no. 34,\r\npp.85-92, 1983.\r\n[2] Yu. L. Menshikov, \u201cThe inverse Problem of Astrodynamics\u201d. Different.\r\nEquations and their Applications in Physics, Dniepropetrovsk,\r\nUniversity, Dniepropetrovsk, Ukraine, pp.19-26, 1990.\r\n[3] C. J. Radcliffe, Jr. C. D. Mote, \u201cIdentification and control of rotating\r\ndisk Vibration\u201d, Trans. ASME: Int. Symp. Syst., Meas. and Control,\r\npp.120-128, 2002.\r\n[4] St. Dubowsky, \u201cActive control of mechanical systems: the state - of the\r\nart for robotics manipulators\u201d, 26th Struct., Struct. Dyn. and Mater.\r\nConf., Orlando, Fla, Apr.15-17, 1985, Pt. 2 .Coll. Techn. Pap. \/ New\r\nYork, N.Y. pp.258-261, 1985.\r\n[5] Yu. L. Menshikov, N. V. Polyakov, \u201cOperative evaluation of unbalance\r\ncharacteristics of a deformable rotor\u201d. In Proc.8th Int. Symp. on\r\nTechnical Diagnostics (IMEKO), Dresden, 23-25 Sept. 1992, pp.399-\r\n408.\r\n[6] Yu. L. Menshikov, \u201cThe influence of uncontrollable inaccuracy of initial\r\ndata on diagnostics results of mechanical objects\u201d, Vibrodiagnostics of\r\nmachines and mechanisms. The Methods and Tools. Zaporozhye,\r\nUkraine, pp.65-66, 1985.\r\n[7] Yu. L. Menshikov,\u201cThe Evaluation of the Unbalance Characteristics of a\r\nRotor by the New Operative Method\u201d, in Proc. of GAMM, 1996, vol.4,\r\npp.103-105.\r\n[8] G. Korn, T. Korn, Mathematical handbook for scientists and engineers,\r\nN.-Y., Toronto, London, 1961.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 104, 2015"}