Lecture 10. 



Solving systems of linear equations using Gaussian elimination/L U decomposition.

It appears that everyone in the class has taken a course in linear algebra and has already seen Gaussian elimination at least once.
Through the use of an example we saw how Gaussian elimination followed by back substitution can be used to solve a system of linear equations. I also presented a slight variant of Gaussian elimination where we save the multipliers so that we can compute a lower triangular matrix L and an upper triangular matrix U such that LU = A. In this way we can use L and U to solve a system Ax = b. We also observed that having L and U at hand allows us to subsequently solve for Ax= bi for any other column vectors bi.
I began the lecture with a problem from the field of chemistry where one determines the components in an ion using mass spectrometry. I have attached a copy of the presentation.

Mass Spectrometry.pdf  

Posted: Mon - October 2, 2006 at 04:58 PM          

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