Geodesic
On a~posteriori approximation of a~set of solutions to a~system of quadratic equations with the use of the Newton method
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 1, pp. 53-65.

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For quadratic systems of algebraic equations we propose an algorithm generating a posteriori estimates of a convex hull of a set of solutions using the results of a step of the Newton method. Results of numerical tests are given. 
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M. Yu. Kokurin; A. I. Kozlov. On a~posteriori approximation of a~set of solutions to a~system of quadratic equations with the use of the Newton method. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 1, pp. 53-65. http://geodesic.mathdoc.fr/item/SJVM_2014_17_1_a4/

[1] Calabi E., “Linear systems of real quadratic forms. II”, Proc. Amer. Math. Soc., 84:3 (1982), 331–334 | DOI | MR | Zbl

[2] Bakhvalov N. C., Zhidkov N. P., Kobelkov G. M., Chislennye metody, BINOM, M., 2007

[3] Godunov S. K., Sovremennye aspekty lineinoi algebry, Nauchnaya kniga, Novosibirsk, 1997 | Zbl

[4] Kokurin M. Yu., “O krivoi P. A. Shirokova i teoremakh Khausdorfa i Dainsa”, Uchenye zapiski Kazanskogo gosudarstvennogo universiteta. Ser. Fiziko-matematicheskie nauki, 151, no. 4, 2009, 51–53 | Zbl

[5] Cowen C. C., Harel E., An Effective Algorithm for Computing the Numerical Range, Technical report, Purdue University, Department of Mathematics, West Lafayette, Indiana, 1995

[6] Morgan A., Solving Polynomial Systems Using Continuation for Engineering and Scientific Problems, Prentice Hall, Englewood Cliffs, N.J., 1987 | MR | Zbl

[7] Koks D., Littl Dzh., O'Shi D., Idealy, mnogoobraziya i algoritmy. Vvedenie v vychislitelnye aspekty algebraicheskoi geometrii i kommutativnoi algebry, Mir, M., 2000

[8] Garloff J., Smith A. P., “Investigation of a subdivision based algorithm for solving systems of polynomial equations”, J. of Nonlinear Analysis, 47:1 (2001), 167–178 | DOI | MR | Zbl