Predicting the Structure of Sparse Orthogonal Factors
نویسندگان
چکیده
The problem of correctly predicting the structures of the orthogo nal factorsQ and R from the structure of a matrix A with full column rank is considered in this paper Recently Hare Johnson Olesky and van den Driessche have described a method to predict these structures and they have shown that corresponding to any speci ed nonzero element in the predicted structures of Q or R there exists a matrix with the given structure whose factor has a nonzero in that position In this paper this method is shown to satisfy a stronger property there exist matrices with the structure of A whose factors have exactly the predicted structures These results use matching theory the Dulmage Mendelsohn decomposition of bipartite graphs and techniques from algebra The proof technique shows that if values are assigned randomly to the nonzeros in A then with high probability the elements predicted to be nonzero in the factors have nonzero values It is shown that this stronger requirement cannot be satis ed for orthogonal factorization with column pivoting In addi tion e cient algorithms for computing the structures of the factors are designed and the relationship between the structure of Q and This author was supported by NSF grant CCR and by U S Department of Energy grant DE FG ER at the Pennsylvania State University and by the Canadian Natural Sciences and Engineering Research Council under grant OGP at the University of Waterloo LINEAR ALGEBRA AND ITS APPLICATIONS xxx xx c Elsevier Science Publishing Co Inc Avenue of the Americas New York NY the Householder array is described
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تاریخ انتشار 2008