Phenomenon of solutions branching in the problems of the objects placement and experimental design

• Autorzy: Grigoriev Y. D.
• Języki publikacji: EN

Abstrakty

EN

The examples of solutions branching are presented in the construction of D- and A-optimal placement of beacons in distance measurement problem of navigation and in the construction of Bayesian and maximin D-efficient designs of experiment..

Słowa kluczowe

EN

solutions branching; bifurcation point; beacon; minimal support; Bayesian and maximin D-efficient experimental designs

• Wydawca: Komisja Informatyki Polskiej Akademii Nauk, Oddział w Gdańsku
• Czasopismo: Metody Informatyki Stosowanej
• Rocznik: 2011
• Tom: nr 5
• Strony: 5--20
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Grigoriev Y. D.

• Department of Computer Science, St.-Petersburg State Electrotechnical University

Bibliografia

• [1] Barabanova L. P. (2008) Optimization of configurations of four beacons in a difference range finding navigation system within the visibility cone (Original Russian Text: Barabanova L. P. published in Izvestiya Akademii Nauk.Teoriya i Sistemy Upravleniya, 2008, No. 4, pp. 90–96.
• [2] Barabanov O. O., Barabanova L. P. Mathematical Problems of Distance Measuring Navigation, Moscow, 2007. (Original Russian Text: Barabanov O. O., Barabanova, L. P. Matematicheskie problemy dalnomernoj navigatsii, Moskva, Fizmatlit, 2007, 272 s.).
• [3] Brӓss D., Dette H. On the number of support points of maximin and Bayesian Doptimal designs in nonlinear regression models. Annals of Statistics, 35(2), 772-792.
• [4] Chaloner K., Larntz K. Optimal Bayesian experimental design applied to logistic regression experiments. J. Statist. Plann. Infer., 1989, 21, 191-208.
• [5] Dette H., Neugebauer H. M. Bayesian optimal one point designs for one parameter nonlinear models. J. Statist. Plann. Inference, 1996, 52, 17-31.
• [6] Keller J. B., Antman S. Bifurcation Theory and Nonlinear Eigenvalue problems / Edited by J.-B.- Keller and S.-Antman, W. A. Benjamin, Inc., New York, Amsterdam, 1969.
• [7] Kiefer J., Wolfowitz J. The equivalence of two extremum problems. Can. J. Math., 12, 129-132.
• [8] Lӓuter Å. Design of experiment method by non-linear parametrization. Math. Operationsforsch. Statist., Ser. Statist., 5, No. 7/8, 1974, 625-636 (in Russian).
• [9] Melas V. B., Staroselsky Yu. M. Studying maximin efficient designs for the Michaelis-Menten model. Procced. St.-Petersburg University, 2007, Series 1, No. 2, 41-50. (Original Russian Text: Melas, V. B., Staroselsky Yu. M. Issledovanie maximin-effektivnykh planov dlya modely Mikhaelisa-Menten. Vestnik Sankt-Peterburgskogo universiteta, 2007, Seriya 1, Vipusk 2, 41-50).
• [10] Reiss E. L. Column buckling – an elementary example of bifurcation.–In: Bifurcation theory and nonlinear eigenvalue problems / Edited by J. B. Keller and S. Antman, W. A. Benjamin, Inc., New York, 1969, Amsterdam.
• [11] Staroselsky Yu. M. Investigation of D-optimal designs for linear-fractional models. Procced. S.-Petersburg University, 2008, Series 10, No. 3, 98-105. (Original Russian Text: Staroselsky Yu. M. Issledovanie bayesovskikh D-optimaljnikh planov dlya drobnolinejnikh modelej. Vestnik Sankt-Peterburgskogo universiteta, 2008, Seriya 10, Vypusk 3, 98-105).
• [12] Staroselsky Yu. M. Investigation of optimal experimental designs for nonlinear regression models. Ph. D. Thesis. St.-Petersburg State University, 2008. (Original Russian Text: Staroselsky Yu. M. Issledovanie optimalynikh planov eksperimenta dlya nelinejnykh po parametram rergessionnykh modelej. St.-Petersburg State University.
• [13] Vainberg M. M., Trenogin V. A. Theory of Branching of Solutions of Non-linear Equations. Monographs and Textbooks on Pure and Applied Mathematics, Noordhoff International Publishing, Leyden, 1974, xxvi+485 pp.
• [14] Wong W. K. A unified approach to the construction of minimax designs. Biometrika, 79, 611-619, 1992.