BIT Numerical Mathematics

, 37:473

Matrix enlarging methods and their application

  • Fernando L. Alvarado

DOI: 10.1007/BF02510237

Cite this article as:
Alvarado, F.L. Bit Numer Math (1997) 37: 473. doi:10.1007/BF02510237


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.

AMS subject classification


Key words

Sparse matrices node splitting orthogonal factorization least squares QR factorization matrix stretching matrix primitization 

Copyright information

© BIT Foundation 1997

Authors and Affiliations

  • Fernando L. Alvarado
    • 1
  1. 1.Department of Electrical and Computer EngineeringThe University of WisconsinMadison

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