Geodesic
A proof of monotony of the Temple quotients in eigenvalue problems
Applications of Mathematics, Tome 29 (1984) no. 2, pp. 149-158

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

If the so-called Collatz method is applied to get twosided estimates of the first eigenvalue $\lambda_1$, the sequences of the so-called Schwarz quatients (which are upper bounds for $\lambda_1$) and of the so-called Temple quotients (which are lower bounds) are constructed. While monotony of the first sequence was proved many years ago, monotony of the second one has been proved only recently by F. goerisch and J. Albrecht in their common paper "Die Monotonie der Templeschen Quotienten" (ZAMM, in print). In the present paper another (so to say elementary) proof is given.
DOI : 10.21136/AM.1984.104078
Classification : 34L99, 35P15, 65L15, 65N25
Keywords: monotony; Collatz method; first eigenvalue; Schwarz quotients; Temple quotients 
@article{10_21136_AM_1984_104078,
     author = {Rektorys, Karel},
     title = {A proof of monotony of the {Temple} quotients in eigenvalue problems},
     journal = {Applications of Mathematics},
     pages = {149--158},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {1984},
     doi = {10.21136/AM.1984.104078},
     mrnumber = {0738500},
     zbl = {0544.65056},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104078/}
}
TY  - JOUR
AU  - Rektorys, Karel
TI  - A proof of monotony of the Temple quotients in eigenvalue problems
JO  - Applications of Mathematics
PY  - 1984
SP  - 149
EP  - 158
VL  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104078/
DO  - 10.21136/AM.1984.104078
LA  - en
ID  - 10_21136_AM_1984_104078
ER  - 
%0 Journal Article
%A Rektorys, Karel
%T A proof of monotony of the Temple quotients in eigenvalue problems
%J Applications of Mathematics
%D 1984
%P 149-158
%V 29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104078/
%R 10.21136/AM.1984.104078
%G en
%F 10_21136_AM_1984_104078
Rektorys, Karel. A proof of monotony of the Temple quotients in eigenvalue problems. Applications of Mathematics, Tome 29 (1984) no. 2, pp. 149-158. doi: 10.21136/AM.1984.104078

Cité par Sources :