Abstract
We establish the exact power order of information complexity for integral equations whose kernels have power singularities and free terms belong to the corresponding Hölder space.
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S. V. Pereverzev and K. Sh. Makhkamov, “Galerkin's information, hyperbolic cross, and complexity of operator equations,”Ukr. Mat. Zh.,43, No. 5, 639–648 (1991).
J. Traub and H. Wozniakowski,General Theory of Optimal Algorithms [Russian translation], Mir, Moscow (1983).
B. G. Gabdulkhaev and V. E. Gorlov, “On the convergence of the polygonal method for the solution of weakly singular integral equations,” in:Functional Analysis and Its Applications [in Russian], Kazan University, Kazan (1975), pp. 60–72.
S. V. Pereverzev and C. C. Schapirov, “Information complexity of equations of the second kind with compact operators in Hilbert space,”J. Complexity,8, 176–202 (1992).
K. I. Babenko, “Some problems in the theory of approximation and numerical analysis,”Usp. Mat. Nauk,40, No. 1, 3–27 (1985).
V. M. Tikhomirov,Some Problems in the Theory of Approximation [in Russian], Moscow University, Moscow (1976).
G. Vainikko, A. Pedas, and P. Uba,Methods for the Solution of Weakly Singular Integral Equations [in Russian], Tartu University, Tartu (1984).
B. S. Kashin and A. A. Saakyan,Orthogonal Series [in Russian], Nauka, Moscow (1984).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.46, No. 11, pp. 1527–1533, November, 1994.
This work was supported by the Foundation for Fundamental Researches of the Ukrainian State Committee on Science and Technology.
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Pereverzev, S.V., Makhkamov, K.S. Information complexity of weakly singular integral equations. Ukr Math J 46, 1688–1694 (1994). https://doi.org/10.1007/BF01058886
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DOI: https://doi.org/10.1007/BF01058886