Linear least squares solutions by householder transformations
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...The Businger and Golub algorithm [8] [20] works well in practice, but there are examples where it fails to produce a factorization satisfying (4) (see Example in 2)....
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...In 2 we review QR with column pivoting [8] [20] and the Chandrasekaran and Ipsen algorithm [13] for computing an RRQR factorization....
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...Golub [20] introduced these factorizations.and, with Businger [8], developed the first algorithm (QR with column pivoting) for computing them....
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...In 7 we show that the concept of a strong RRQR factorization is not completely new in that the QR factorizati0n given by the Businger and Golub algorithm [8] [20] satisfies (5) and (6) with q (k, n) and q2(k, n) functions that grow exponentially with k. Finally, in 8 we present some extensions of this work, including a version of Algorithm 5 that is nearly as fast as QR with column pivoting for most problems and takes O (mn2) floating-point operations in the worst case....
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...QR with column pivoting [8] [20] is a modification of the ordinary QR algorithm....
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"Linear least squares solutions by h..." refers methods in this paper
...A very effective method to realize the decomposition (t) is via Householder transformations [ 1 ]....
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"Linear least squares solutions by h..." refers background in this paper
...m. It can be shown, cf. [ 2 ], that p(k) is generated as follows:...
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