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Topic: How to find a bounding line?
Replies: 39   Last Post: Jul 12, 2013 5:39 AM

 Messages: [ Previous | Next ]
 Woody Posts: 44 Registered: 7/29/09
Re: How to find a bounding line?
Posted: Jul 10, 2013 1:52 PM

On Sunday, July 7, 2013 6:43:41 PM UTC-7, quasi wrote:
> To show that, assume an optimal line L with slope a passes through
> the point (x_k,y_k).
>
> By the point-slope formula, the line has the equation

...
> y = a*x + (y_k - a*x_k)
>
> Let s = SUM(y_i - y(x_i)).
>
> Since L is an optimal bounding line, s is minimal, hence a change
> in the value of a, if it doesn't break the bounding condition,
> cannot decrease the sum.
>
> But the sum s is at most linear as a function of a.
> Case (1): s is degree 1 as function of a.
> If L does not pass through any of the other N-1 points, a
> sufficiently small positive or negative change in a will decrease
> the value of s

This is not correct. A small change in a can either increase or decrease s, depending on the values x_i. Whether L passes through any of the other points is irrelevant.

Date Subject Author
7/7/13 Woody
7/7/13 Scott Berg
7/7/13 Peter Percival
7/7/13 Woody
7/7/13 quasi
7/7/13 quasi
7/8/13 quasi
7/8/13 Woody
7/8/13 quasi
7/8/13 LudovicoVan
7/8/13 LudovicoVan
7/10/13 Woody
7/10/13 quasi
7/8/13 Leon Aigret
7/8/13 Woody
7/10/13 Leon Aigret
7/10/13 Leon Aigret
7/10/13 Woody
7/10/13 RGVickson@shaw.ca
7/10/13 Woody
7/10/13 quasi
7/7/13 quasi
7/7/13 quasi
7/7/13 quasi
7/8/13 William Elliot
7/8/13 Peter Percival
7/8/13 quasi
7/11/13 Woody
7/11/13 quasi
7/11/13 LudovicoVan
7/11/13 quasi
7/11/13 Leon Aigret
7/11/13 Woody
7/11/13 Leon Aigret
7/12/13 Woody
7/12/13 Leon Aigret
7/11/13 Woody
7/12/13 quasi
7/12/13 Woody
7/12/13 quasi