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# How to find a good approximation of : LINPACK METHOD

is the unit eigenvector corresponding to . We need this vector in the hard case (see the paragraph containing equation 4.15 ). Since is the eigenvector corresponding to , we can write:

We will try to find a vector which minimizes . This is equivalent to find a vector which maximize . We will choose the component of between and in order to make large. This is achieved by ensuring that at each stage of the forward substitution , the sign of is chosen to make as large as possible. In particular, suppose we have determined the first components of during the forward substitution, then the component satisfies:

and we pick to be depending on which of

is larger. Having found , is simply . The vector found this way has the useful property that

as

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Frank Vanden Berghen 2004-04-19