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from which we obtain the relation
zi = ~i BOA vi. (17)
Hence, xi can be computed from the corresponding
vi
by multiplication with B?A, which
can be performed by means of the algorithm from the previous section.
Notice that the vectors ui and
xi
for i = p+ 1,..., n cannot be determined by our Lanczos
algorithm. However, the spaces span{xp+i,..., xn} and span{up+i,..., un}--which may be
more important than the vectors--are spanned by the columns of the two matrices W and
A W, respectively. Moreover, the vector
9 o = ~
~Tb
~i,
i..---p+l
which is the component of the regularized ...