Geodesic
A convergent nonlinear splitting via orthogonal projection
Applications of Mathematics, Tome 29 (1984) no. 4, pp. 250-257

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We study the convergence of the iterations in a Hilbert space $V,x_{k+1}=W(P)x_k, W(P)z=w=T(Pw+(I-P)z)$, where $T$ maps $V$ into itself and $P$ is a linear projection operator. The iterations converge to the unique fixed point of $T$, if the operator $W(P)$ is continuous and the Lipschitz constant $\left\|(I-P)W(P)\right\|1$. If an operator $W(P_1)$ satisfies these assumptions and $P_2$ is an orthogonal projection such that $P_1P_2=P_2P_1=P_1$, then the operator $W(P_2)$ is defined and continuous in $V$ and satisfies $\left\|(I-P_2)W(P_2)\right\|\leq \left\|(I-P_1)W(P_1)\right\|$.
DOI : 10.21136/AM.1984.104093
Classification : 47H10, 47H17, 47J25, 65J15
Keywords: convergent nonlinear splitting; orthogonal projection; iterations; Hilbert space; fixed point 
@article{10_21136_AM_1984_104093,
     author = {Mandel, Jan},
     title = {A convergent nonlinear splitting via orthogonal projection},
     journal = {Applications of Mathematics},
     pages = {250--257},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {1984},
     doi = {10.21136/AM.1984.104093},
     mrnumber = {0754077},
     zbl = {0613.65060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104093/}
}
TY  - JOUR
AU  - Mandel, Jan
TI  - A convergent nonlinear splitting via orthogonal projection
JO  - Applications of Mathematics
PY  - 1984
SP  - 250
EP  - 257
VL  - 29
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104093/
DO  - 10.21136/AM.1984.104093
LA  - en
ID  - 10_21136_AM_1984_104093
ER  - 
%0 Journal Article
%A Mandel, Jan
%T A convergent nonlinear splitting via orthogonal projection
%J Applications of Mathematics
%D 1984
%P 250-257
%V 29
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104093/
%R 10.21136/AM.1984.104093
%G en
%F 10_21136_AM_1984_104093
Mandel, Jan. A convergent nonlinear splitting via orthogonal projection. Applications of Mathematics, Tome 29 (1984) no. 4, pp. 250-257. doi: 10.21136/AM.1984.104093

Cité par Sources :