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Topic: How to solve linear equation with linear constraints
Replies: 6   Last Post: Jun 23, 2006 7:40 PM

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 Toni Lassila Posts: 536 Registered: 12/13/04
Re: How to solve linear equation with linear constraints
Posted: Jun 23, 2006 11:47 AM

On 23 Jun 2006 08:22:23 -0700, "C6L1V@shaw.ca" <C6L1V@shaw.ca> wrote:

>hmobahi@gmail.com wrote:
>> Hi Folks,
>>
>> I am interested in the equation of form:
>> a1*x1+a2*x2+a3*x3+...an*xn + b = 0
>> where "a1...an" and "b" are given and "x1...xn" are n unknown
>> variables. Obviously, the system has n unknowns and only one equation.
>> This equation comes with a set of constraints of form:
>> -1<xi<1 where i = 1, ...n.

>
>Do you really mean -1 < xi < 1, or do you actually mean -1 <= xi <= 1?
>This makes a tremendous difference. With non-strict inequalities, you
>have an extensive and powerful theory of linear programming available
>to you, but with strict inequalities this is not the case. It is
>possible that your problem has no solution at all if you use "<", but
>has easily-obtained solutions if you use "<=".

It's not an optimization problem. Of course there are solutions if
sum_i |a_i| > |b|.

Date Subject Author
6/23/06 hmobahi@gmail.com
6/23/06 Michael JÃÂ¸rgensen
6/23/06 C6L1V@shaw.ca
6/23/06 Toni Lassila
6/23/06 Randy Poe
6/23/06 C6L1V@shaw.ca
6/23/06 Robert Israel