Consider the problem of solving overdetermined system(adsbygoogle = window.adsbygoogle || []).push({});

Ax = b;

In the problem I am trying to solve (from the field of spectral unmixing) number of unknowns usually varies between N = 2 and 5 and the matrix A is typically 10 by N. However, now the choice of matrix A is fully user-dependent. (For information, it is a so called molar absorption matrix, which is populated with the absorption spectra with N columns corresponding to individual

absorbers and M rows corresponding to the optical wavelengths. Typical example of such matrix would be hemoglobin absorption spectra http://www.surgicalneurologyint.com/viewimage.asp?img=SurgNeurolInt_2010_1_1_75_73316_u2.jpg [Broken])

I envision some algorithm where I could decide which row of this matrix can be excluded and the system can still be solved.

Do you know if there is any criterion which tells me that removal of one row is less critical than removal of another for accuracy of solution?

Thank you!

Elena

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# Criterion of removal of equations from overdetermined system

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