A proof of monotony of the Temple quotients in eigenvalue problems

Karel Rektorys

Aplikace matematiky (1984)

  • Volume: 29, Issue: 2, page 149-158
  • ISSN: 0862-7940

Abstract

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If the so-called Collatz method is applied to get twosided estimates of the first eigenvalue λ 1 , the sequences of the so-called Schwarz quatients (which are upper bounds for λ 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.

How to cite

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Rektorys, Karel. "A proof of monotony of the Temple quotients in eigenvalue problems." Aplikace matematiky 29.2 (1984): 149-158. <http://eudml.org/doc/15342>.

@article{Rektorys1984,
abstract = {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.},
author = {Rektorys, Karel},
journal = {Aplikace matematiky},
keywords = {monotony; Collatz method; first eigenvalue; Schwarz quotients; Temple quotients; monotony; Collatz method; first eigenvalue; Schwarz quotients; Temple quotients},
language = {eng},
number = {2},
pages = {149-158},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A proof of monotony of the Temple quotients in eigenvalue problems},
url = {http://eudml.org/doc/15342},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Rektorys, Karel
TI - A proof of monotony of the Temple quotients in eigenvalue problems
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 2
SP - 149
EP - 158
AB - 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.
LA - eng
KW - monotony; Collatz method; first eigenvalue; Schwarz quotients; Temple quotients; monotony; Collatz method; first eigenvalue; Schwarz quotients; Temple quotients
UR - http://eudml.org/doc/15342
ER -

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