, Volume 37, Issue 3, pp 473-505

Matrix enlarging methods and their application

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Abstract

This paper explores several methods for matrix enlarging, where an enlarged matrixà 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.à can exhibit several desirable properties. For example,à 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 fill-in in theR matrix which occurs during orthogonal factorization as a result of dense rows. Numerical experiments support these conjectures.

This paper elaborates on a presentation at the International Linear Algebra Year conference in Toulouse, France, September 1995. The author is grateful to CERFACS for support. Support by NSF grants ECS-9216308 and ECS-9215271 is also acknowledged.