RO EN
On a class of nonlocal generalized splines. (Russian)
Authors: Verlan Igor
\gather
S(x,u)=f_{i+1}\nu (t,u)+f_i(1-\nu (t,u))+h_im_i(2t-t^2-\nu (t,u))
\bigm / 2+ \\
+h_im_{i+1}(t^2-\nu(t,u))\bigm /2,
\endgather
$$
or
$$
\gather
S(x,u)=f_{i+1}t+f_i(1-t)+h^2_i\{M_i(2t-2\nu (t,u_i)-t\nu'' (1,u_i)+
t^2\nu'' (1,u_i))- \\
- M_{i+1}(2t-2\nu (t,u_i)-t\nu'' (0,u_i)+
t^2\nu'' (0,u_i)) \} \bigm /2(\nu'' (1,u_i)-\nu''(0,u_i)),
\endgather
$$
where $t=(x-x_{i-1})/h_i$, $h_i=x_{i+1}-x_i$, $u$ -- the free parametrs vector. $s'(x_i)=m_i$, $s''(x_i)=M_i$, $i=0,(1),n$ and $\nu(t,u)\in \Cal L$, where $\Cal L=\{\varphi (t,u):\varphi (t,u)\in c^2[a,b]; \ \varphi (1,u)=1, \ \varphi (0,u)=\varphi' (1,u)=0\}$. Different interpolation splynes can be obtained by the chose of function $\nu (t,u)$. The determination of unknow coefficients systems are presented.
Abstract
The interpolation problem of $f_i$, $i=0, (1),n$ on the mech $\bigtriangleup : a=x_0\gather
S(x,u)=f_{i+1}\nu (t,u)+f_i(1-\nu (t,u))+h_im_i(2t-t^2-\nu (t,u))
\bigm / 2+ \\
+h_im_{i+1}(t^2-\nu(t,u))\bigm /2,
\endgather
$$
or
$$
\gather
S(x,u)=f_{i+1}t+f_i(1-t)+h^2_i\{M_i(2t-2\nu (t,u_i)-t\nu'' (1,u_i)+
t^2\nu'' (1,u_i))- \\
- M_{i+1}(2t-2\nu (t,u_i)-t\nu'' (0,u_i)+
t^2\nu'' (0,u_i)) \} \bigm /2(\nu'' (1,u_i)-\nu''(0,u_i)),
\endgather
$$
where $t=(x-x_{i-1})/h_i$, $h_i=x_{i+1}-x_i$, $u$ -- the free parametrs vector. $s'(x_i)=m_i$, $s''(x_i)=M_i$, $i=0,(1),n$ and $\nu(t,u)\in \Cal L$, where $\Cal L=\{\varphi (t,u):\varphi (t,u)\in c^2[a,b]; \ \varphi (1,u)=1, \ \varphi (0,u)=\varphi' (1,u)=0\}$. Different interpolation splynes can be obtained by the chose of function $\nu (t,u)$. The determination of unknow coefficients systems are presented.
Contents
- Countably compact topologies on Boolean rings. (Russian)
- Locally dissipative dynamical systems and some of their applications. (Russian)
- Conditions for the maximal multiplicity of an integral line of a differential system with homogeneities of $m$th order. (Russian)
- On the spectrum in the right half-plane of a class of operator pencils. (Russian)
- K-loops. (Russian)
- Groups of automorphisms of medial quasigroups and medial fields. (Russian)
- On the spectrum of perturbed differential operators with periodic coefficients. (Russian)
- Parametric completeness in the logic of the simplest pseudo-Boolean algebra with incomparable elements. (Russian)
- Coefficient conditions for the coexistence of two singular points of summed multiplicity 4 in a finite part of a phase plane of a quadratic system. (Russian)
- On the kinds of two-dimensional multiregular partitions. (Russian)
- On a class of nonlocal generalized splines. (Russian)
- On the number of near neighbors in regular partitions of Lobachevskij space by compact polyhedra. (Russian)
- An approximation algorithm for matroids with coalitions. (English)
- On finite projection of nonstationary $M/GI/1$ queueing systems. (English)
- Numerical modeling of the process of high-velocity penetration of an obstacle. (Russian)
