 | | From: | daniel.wolff at csfb.com | | Subject: | tighter bound on square-root inequality | | Date: | 23 Jan 2005 19:50:52 -0800 |
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 | Hello,
anyone out there have a tighter bound on the inequality
\Sum_{i=1}^n \sqrt(a_i)\leq n*\sqrt(\Sum_{i=1}^n a_i).
I have seen people citing a bound of \sqrt(n) on the right hand side
but cannot demonstrate it and would like something tighter.
Thank you.
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| | From: | Jannick Asmus | | Subject: | Re: tighter bound on square-root inequality | | Date: | Mon, 24 Jan 2005 04:58:39 +0100 |
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| On 1/24/2005 4:50 AM, daniel.wolff@csfb.com wrote:
> Hello,
>
> anyone out there have a tighter bound on the inequality
>
> \Sum_{i=1}^n \sqrt(a_i)\leq n*\sqrt(\Sum_{i=1}^n a_i).
>
> I have seen people citing a bound of \sqrt(n) on the right hand side
> but cannot demonstrate it and would like something tighter.
> Thank you.
>
Apply the Cauchy-Schwarz inequality to (1,...,1) and
(sqrt(a1),...,sqrt(an)).
J.
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| | From: | daniel.wolff at csfb.com | | Subject: | Re: tighter bound on square-root inequality | | Date: | 23 Jan 2005 20:11:41 -0800 |
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| Thank you J. I forgot this trick.
Can this factor of \sqrt(n) be tightened?
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| | From: | Jannick Asmus | | Subject: | Re: tighter bound on square-root inequality | | Date: | Mon, 24 Jan 2005 05:20:51 +0100 |
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| On 1/24/2005 5:11 AM, daniel.wolff@csfb.com wrote:
> Thank you J. I forgot this trick.
> Can this factor of \sqrt(n) be tightened?
>
No, since Cauchy-Schwarz is tight already.
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