Epsilon-inflation with contractive interval functions

Günter Mayer

Applications of Mathematics (1998)

  • Volume: 43, Issue: 4, page 241-254
  • ISSN: 0862-7940

Abstract

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For contractive interval functions [ g ] we show that [ g ] ( [ x ] ϵ k 0 ) ⊆ ∫ ( [ x ] ϵ k 0 ) results from the iterative process [ x ] k + 1 : = [ g ] ( [ x ] ϵ k ) after finitely many iterations if one uses the epsilon-inflated vector [ x ] ϵ k as input for [ g ] instead of the original output vector [ x ] k . Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.

How to cite

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Mayer, Günter. "Epsilon-inflation with contractive interval functions." Applications of Mathematics 43.4 (1998): 241-254. <http://eudml.org/doc/33010>.

@article{Mayer1998,
abstract = {For contractive interval functions $ [g] $ we show that $ [g]([x]^\{k_0\}_\epsilon ) \subseteq \int ([x]^\{k_0\}_\epsilon ) $ results from the iterative process $ [x]^\{k+1\} := [g]([x]^k_\epsilon ) $ after finitely many iterations if one uses the epsilon-inflated vector $ [x]^k_\epsilon $ as input for $ [g] $ instead of the original output vector $ [x]^k $. Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.},
author = {Mayer, Günter},
journal = {Applications of Mathematics},
keywords = {epsilon-inflation; P-contraction; contraction; verification algorithms; interval computation; nonlinear equations; eigenvalues; singular values; P-contraction; interval computation; nonlinear equations},
language = {eng},
number = {4},
pages = {241-254},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Epsilon-inflation with contractive interval functions},
url = {http://eudml.org/doc/33010},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Mayer, Günter
TI - Epsilon-inflation with contractive interval functions
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 4
SP - 241
EP - 254
AB - For contractive interval functions $ [g] $ we show that $ [g]([x]^{k_0}_\epsilon ) \subseteq \int ([x]^{k_0}_\epsilon ) $ results from the iterative process $ [x]^{k+1} := [g]([x]^k_\epsilon ) $ after finitely many iterations if one uses the epsilon-inflated vector $ [x]^k_\epsilon $ as input for $ [g] $ instead of the original output vector $ [x]^k $. Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way.
LA - eng
KW - epsilon-inflation; P-contraction; contraction; verification algorithms; interval computation; nonlinear equations; eigenvalues; singular values; P-contraction; interval computation; nonlinear equations
UR - http://eudml.org/doc/33010
ER -

References

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