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Peter FRANEK
Zerosexperiments
Commits
c4375c26
Commit
c4375c26
authored
Feb 14, 2017
by
Peter FRANEK
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title change, small corrections
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c4375c26
...
@@ 171,7 +171,7 @@ grestore
...
@@ 171,7 +171,7 @@ grestore
%
%
\begin{document}
\begin{document}
\title
{
Solving Equations
with Inherent
Uncertainty
\thanks
{
The research
\title
{
Solving Equations
and Optimization Problems with
Uncertainty
\thanks
{
The research
leading to these results has received funding from Austrian Science Fund (FWF): M 1980 and
leading to these results has received funding from Austrian Science Fund (FWF): M 1980 and
from the Czech Science Foundation (GACR) grant number 1514484S with institutional support RVO:67985807.
}
from the Czech Science Foundation (GACR) grant number 1514484S with institutional support RVO:67985807.
}
}
}
...
@@ 748,7 +748,7 @@ If we include, in the coboundary matrix, only columns corresponding to $(n1)$s
...
@@ 748,7 +748,7 @@ If we include, in the coboundary matrix, only columns corresponding to $(n1)$s
order the rows (
$
n
$
simplices) by the
$
u
$
filtration, and then
order the rows (
$
n
$
simplices) by the
$
u
$
filtration, and then
perform a column matrix reduction such that, after the reduction, the lowest nonzero element in each column is the last nonzero element in that row,
perform a column matrix reduction such that, after the reduction, the lowest nonzero element in each column is the last nonzero element in that row,
then the desired
$
\beta
$
is the filtration value corresponding to the row of the lowest nonzero element on the right hand side after the reduction.
}
,
then the desired
$
\beta
$
is the filtration value corresponding to the row of the lowest nonzero element on the right hand side after the reduction.
}
,
we compute the
small
est
$
\beta
$
such that
$
f'
_{
A
_{
r
}
\cap
u
_
\beta
}$
is not extendable: by Section~
\ref
{
sec:algorithmoracle
}
we compute the
larg
est
$
\beta
$
such that
$
f'
_{
A
_{
r
}
\cap
u
_
\beta
}$
is not extendable: by Section~
\ref
{
sec:algorithmoracle
}
the robustness of zero of
$
f
$
on
$
u
_{
\beta
}$
is at least
$
r

\alpha
>
0
$
and
the robustness of zero of
$
f
$
on
$
u
_{
\beta
}$
is at least
$
r

\alpha
>
0
$
and
\begin{equation*}
\begin{equation*}
\beta
\leq
\inf
_{
\
gf
\\leq
r
\alpha
}
\,\,\max
_{
x
\in
g
^{
1
}
(0)
}
u(x)
\leq
\max
_{
x
\in
f
^{
1
}
(0)
}
\,
u(x).
\beta
\leq
\inf
_{
\
gf
\\leq
r
\alpha
}
\,\,\max
_{
x
\in
g
^{
1
}
(0)
}
u(x)
\leq
\max
_{
x
\in
f
^{
1
}
(0)
}
\,
u(x).
...
...
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