Estimation of Distance [closed]
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Let $x,xi_0, xi_varepsilon in mathbb{R}^2$.
What is the function $F_{xi}$ in the following equation and how do you get the final result?
$$mathrel{bigg|}frac{xi_varepsilon - x}{mid xi_varepsilon - x mid^2} - frac{xi_0 - x}{mid xi_0 - x mid^2}mathrel{bigg|} = mathrel{bigg|}int_0^1langle,F_xi[xi_0+t(xi_varepsilon-xi_0)],xi_varepsilon-xi_0rangle dtmathrel{bigg|}$$
$$leq 2midxi_varepsilon-xi_0midint_0^1frac{1}{mid,x-xi_tmid^2}dtleq 2frac{midxi_varepsilon -xi_0mid^lambdamidxi_varepsilon -xi_0mid^{1-lambda}}{minmid x-xi_tmid^2}.$$
real-analysis
asked Nov 18 at 12:08
MrIndianaJones
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closed as unclear what you're asking by amWhy, user90369, user10354138, Shailesh, Cesareo Nov 20 at 1:16
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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Let $x,xi_0, xi_varepsilon in mathbb{R}^2$.
What is the function $F_{xi}$ in the following equation and how do you get the final result?
$$mathrel{bigg|}frac{xi_varepsilon - x}{mid xi_varepsilon - x mid^2} - frac{xi_0 - x}{mid xi_0 - x mid^2}mathrel{bigg|} = mathrel{bigg|}int_0^1langle,F_xi[xi_0+t(xi_varepsilon-xi_0)],xi_varepsilon-xi_0rangle dtmathrel{bigg|}$$
$$leq 2midxi_varepsilon-xi_0midint_0^1frac{1}{mid,x-xi_tmid^2}dtleq 2frac{midxi_varepsilon -xi_0mid^lambdamidxi_varepsilon -xi_0mid^{1-lambda}}{minmid x-xi_tmid^2}.$$
real-analysis
asked Nov 18 at 12:08
MrIndianaJones
1
closed as unclear what you're asking by amWhy, user90369, user10354138, Shailesh, Cesareo Nov 20 at 1:16
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 18 at 12:15
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up vote
0
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up vote
0
down vote
favorite
Let $x,xi_0, xi_varepsilon in mathbb{R}^2$.
What is the function $F_{xi}$ in the following equation and how do you get the final result?
$$mathrel{bigg|}frac{xi_varepsilon - x}{mid xi_varepsilon - x mid^2} - frac{xi_0 - x}{mid xi_0 - x mid^2}mathrel{bigg|} = mathrel{bigg|}int_0^1langle,F_xi[xi_0+t(xi_varepsilon-xi_0)],xi_varepsilon-xi_0rangle dtmathrel{bigg|}$$
$$leq 2midxi_varepsilon-xi_0midint_0^1frac{1}{mid,x-xi_tmid^2}dtleq 2frac{midxi_varepsilon -xi_0mid^lambdamidxi_varepsilon -xi_0mid^{1-lambda}}{minmid x-xi_tmid^2}.$$
real-analysis
asked Nov 18 at 12:08
MrIndianaJones
1
Let $x,xi_0, xi_varepsilon in mathbb{R}^2$.
What is the function $F_{xi}$ in the following equation and how do you get the final result?
$$mathrel{bigg|}frac{xi_varepsilon - x}{mid xi_varepsilon - x mid^2} - frac{xi_0 - x}{mid xi_0 - x mid^2}mathrel{bigg|} = mathrel{bigg|}int_0^1langle,F_xi[xi_0+t(xi_varepsilon-xi_0)],xi_varepsilon-xi_0rangle dtmathrel{bigg|}$$
$$leq 2midxi_varepsilon-xi_0midint_0^1frac{1}{mid,x-xi_tmid^2}dtleq 2frac{midxi_varepsilon -xi_0mid^lambdamidxi_varepsilon -xi_0mid^{1-lambda}}{minmid x-xi_tmid^2}.$$
real-analysis
real-analysis
asked Nov 18 at 12:08
MrIndianaJones
1
asked Nov 18 at 12:08
MrIndianaJones
1
asked Nov 18 at 12:08
MrIndianaJones
1
asked Nov 18 at 12:08
MrIndianaJones
1
asked Nov 18 at 12:08
MrIndianaJones
1
1
closed as unclear what you're asking by amWhy, user90369, user10354138, Shailesh, Cesareo Nov 20 at 1:16
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
closed as unclear what you're asking by amWhy, user90369, user10354138, Shailesh, Cesareo Nov 20 at 1:16
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 18 at 12:15
add a comment |
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 18 at 12:15
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 18 at 12:15
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 18 at 12:15
add a comment |
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
Nov 18 at 12:15