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SVD and Signal Processing, III
book

SVD and Signal Processing, III

by M. Moonen, B. De Moor
March 1995
Intermediate to advanced content levelIntermediate to advanced
498 pages
23h 58m
English
Elsevier Science
Content preview from SVD and Signal Processing, III
162
C. - T. Pan and P. T. P. Tang
Moreover, ak(A) and ak+l(A) can be estimated by the quantities
r(R11)
and
y(R22):
<_ <_ +
and
+ k)) _<
_<
k
In other words, the conclusions (5), (6), (7) and (8) of Lemmas 2 and 3 are all satisfied
with f = 1. More generally, if Rlx is an .f-pivoted block, 0 < .f < 1, then (5), (6), (7)
and (8) are all satisfied with the relaxation factor f.
In particular, if A has numerical rank k, we have a rank-revealing QR factorization with
O'min(.~ll )
~>
(f/~/k(n- k + 1))ak(A)
and O'max(R22 )
<: (~/(n-
k)(k + 1)/f)ak+l(A).
(See [6] for a proof).
Now we ...
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Publisher Resources

ISBN: 9780444821072