Abstract
An algebra over recognition algorithms supplemented with a normalization operation (under various definitions) and the division operation is investigated. Correctness criteria for various algebraic closures are obtained.
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References
Yu. I. Zhuravlev, “Correct Algorithms over Sets of Incorrect (Heuristic) Algorithms: Part II,” Kibernetika, No. 6, 21–27 (1977).
Yu. I. Zhuravlev, “An Algebraic Approach to Recognition and Classification Problems,” in Problems of Cybernetics, issue 33 (Nauka, Moscow, 1978; Hafner, 1986), pp. 5–68.
A. G. D’yakonov, “An Algebra over Estimation Algorithms: The Minimal Degree of Correct Algorithms,” Zh. Vychisl. Mat. Mat. Fiz. 45 1134–1145 (2005) [Comput. Math. Math. Phys. 45, 1095–1106 (2005)].
Yu. I. Zhuravlev and V. V. Nikiforov, “Recognition Algorithms Based on Estimate Evaluation,” Kibernetika, No. 3, 1–11 (1971).
A. G. D’yakonov, “An Algebra over Estimation Algorithms: Monotone Decision Rules,” Zh. Vychisl. Matem. Mat. Fiz. 45, 1893–1904 (2005) [Comput. Math. Math. Phys. 45, 1822–1833 (2005)].
V. A. Il’in and G. D. Kim, Linear Algebra and Analytical Geometry: Textbook (Mosk. Gos. Univ., Moscow, 1998) [in Russian].
V. L. Matrosov, “On Completeness Criteria for the Model of Estimation Algorithms and Its Agebraic Closure,” Dokl. Akad. Nauk SSSR 258, 791–796 (1981).
V. L. Matrosov, “Correct Algebras of Limited Capacity over Estimation Algorithms,” Zh. Vychisl. Mat. Mat. Fiz. 21, 1276–1291 (1981).
I. V. Proskuryakov, Problem Book in Linear Algebra (Nauka, Moscow, 1970) [in Russian].
A. G. D’yakonov, Algebra over Estimation Algorithms: Textbook (Mosk. Gos. Univ., Moscow, 2006) [in Russian].
C. A. Micchelli, “Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions,” Construct. Approximat. 2, 11–22 (1986).
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Original Russian Text © A.G. D’yakonov, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 6, pp. 1099–1109.
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D’yakonov, A.G. Algebra over estimation algorithms: Normalization and division. Comput. Math. and Math. Phys. 47, 1050–1060 (2007). https://doi.org/10.1134/S0965542507060140
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DOI: https://doi.org/10.1134/S0965542507060140