Matrix enlarging methods and their application
 Fernando L. Alvarado
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This paper explores several methods for matrix enlarging, where an enlarged matrixÃ is constructed from a given matrixA. The methods explored include matrix primitization, stretching and node splitting. Graph interpretations of these methods are provided. Solving linear problems using enlarged matrices yields the answer to the originalAx=b problem.Ã can exhibit several desirable properties. For example,Ã can be constructed so that the valence of any row and/or column is smaller than some desired number (≥4). This is beneficial for algorithms that depend on the square of the number of entries of a row or column. Most particularly, matrix enlarging can results in a reduction of the fillin in theR matrix which occurs during orthogonal factorization as a result of dense rows. Numerical experiments support these conjectures.
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 Title
 Matrix enlarging methods and their application
 Journal

BIT Numerical Mathematics
Volume 37, Issue 3 , pp 473505
 Cover Date
 19970901
 DOI
 10.1007/BF02510237
 Print ISSN
 00063835
 Online ISSN
 15729125
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 65F20
 Sparse matrices
 node splitting
 orthogonal factorization
 least squares
 QR factorization
 matrix stretching
 matrix primitization
 Industry Sectors
 Authors

 Fernando L. Alvarado ^{(1)}
 Author Affiliations

 1. Department of Electrical and Computer Engineering, The University of Wisconsin, Madison