http://vmath.ru/vf5/ 2026-10-13T03:43:04+0300 http://vmath.ru/vf5/ http://vmath.ru/vf5/lib/tpl/vf5/images/favicon.ico text/html 2021-06-03T23:07:16+0300 Anonymous (anonymous@undisclosed.example.com) http://vmath.ru/vf5/matricese/optimize/distancee/apollonius_e?rev=1622750836&do=diff Author --- Русская версия ---------- Distance evaluation between geometric objects ---------- --- ---- Distance from a point to an ellipse or an ellipsoid We discuss here the consequences in $ \mathbb R^{3} $ of the general result on the distance evaluation from a point to a quadric in $ {\mathbb R}^{n} $. The main task here is to detalize the algorithms for computation of the distance equation and for finding the nearest (and the farthest) point coordinates in the ellipse or ellipsoid. $… text/html 2025-02-10T12:15:52+0300 Anonymous (anonymous@undisclosed.example.com) http://vmath.ru/vf5/matricese/optimize/distancee/casc2022ex?rev=1739178952&do=diff Author Computational results for the paper Kalinina E., Uteshev A. On the Real Stability Radius for Some Classes of Matrices. LNCS, 2021, V. 12865, pp. 192-208 $$ A=\left(\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -91 & -55 & -13 \end{array} \right); \quad \mbox{spectrum} \ \{- 7 , - 3 \pm 2 \mathbf i\} \ ; $$ $$ \mathcal F(z) := 33076090700402342058246544\,z^6-377039198861306289080145178864\, z^5 $$ $$ +937864902703881321034450183916\,z^4-771868276098720970149792503999\,z^3+211070978787… text/html 2026-06-06T21:11:23+0300 Anonymous (anonymous@undisclosed.example.com) http://vmath.ru/vf5/matricese/optimize/distancee/torri_e?rev=1780769483&do=diff Русская версия ---------- Distance evaluation between geometric objects ---------- Fermat-Torricelli problem and its development Generalized Fermat-Torricelli problem Problem. Given the coordinates of $ K_{} $ points in $ \mathbb R^{n}_{} $ : $ \{P_j=(x_{j1},\dots,x_{jn})\}_{j=1}^K $ and the real numbers $ \{ m_j \}_{j=1}^K $, find the coordinates of the point $ P_{\ast}=(x_{\ast 1},\dots,x_{\ast n}) $ solving the following optimization problem: $$ \min_{P\in \mathbb R^n} F(P) \qquad fo…