Re: help for least squares

[andrea console]

hi Ed,

the problem is that, without constrain, I don't get the solution I expect but a very different one that is not suitable for my purpose.

My real problem is something like:

b = (A*x)*y+z (x,y and z unknown)

 that I semplified in

b = s*y+z (y and z unknown and s my best guess of A*x)

with a lot of additive noise.

2013/6/22 Ed Meyer <address@hidden>

On Sat, Jun 22, 2013 at 6:42 AM, andrea console <address@hidden> wrote:

I have to solve, in least squares sense, a system of equations like:

b_1 = [a_1, 1]*[x;y];

b_2 = [a_2, 1]*[x;y];

b_3 = [a_3, 1]*[x;y];

b_4 = [a_4, 1]*[x;y];

...

b_n = [a_n, 1]*[x;y];

where b_i and a_i are sperimental values, thus affected by various sources of error.

I know that 0<x<1 and nothing about y (apart that it should be quite small).

How I can find the best solution that meets this conditions?

thanks

Is it the uncertainty in a_i and b_i you are worried about? otherwise can't
you just use z = A\b where z=[x;y]?
Account for the uncertainty is difficult to do accurately; see e.g.

http://www.nsc.ru/interval/Library/Thematic/DataProcs/MarkovILS.pdf

--
Ed Meyer