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rmatrixsolvels gives different answer for the same problem? http://forum.alglib.net/viewtopic.php?f=2&t=766	Page 1 of 1

Author:	shale [ Thu Jan 31, 2013 10:36 pm ]
Post subject:	rmatrixsolvels gives different answer for the same problem?
Hi all, I'm a newbiew to this forum. I encountered a problem when using the function rmatrixsolvels to solve a overdetermined Ax = b problem. The purpose is solving two unknowns, u1 and u2. The equation is as this format G = u1 P / (P + u2). G and P are both observed from real experiments. The equation above can be transformed into two different formats as below. Format 1 P * u1 - p * u2 = G * P Format 2 p * 1 / u1 + u2 / u1 = P / G. In Format 2, I set 1 / u1 as x1, and u2 / u1 as x2, so for Ax = b, the equation is like G x1 + x2 = P/G Clearly, A[i, 0] = Gi, A[i, 1] = 1; b[i] = Pi/Gi, i = 1,2,..,m data points Then I used rmatrixsolvels to solve the problem and got the exact answers I want. However, if I follow Format 1, A[i, 0] = Pi, A[i, 1] = -Gi; b[i] = Gi * Pi, Then I used rmatrixsolvels and got totally different answers! I'm wondering when we use rmatrixsolvels, should one column in matrix A be always 1? Is that why my Format 2 failed? Per my poor knowledge on least-square method, the equation is x0 + x1t1 + x2 t2 .... = y. Does that mean the coefficient for x0, is 1 by default? It may be more like a math rather than coding quesiton. Any comments appreciated!

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