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Pivot selection and row ordering in Givens reduction on sparse matrices. (English) Zbl 0298.65029


MSC:

65F30 Other matrix algorithms (MSC2010)
65F05 Direct numerical methods for linear systems and matrix inversion
Full Text: DOI

References:

[1] Curtis, A. R., Reid, J. K.: The solution of large sparse unsymmetric systems of linear equations. J. IMA8, 344–353 (1971). · Zbl 0229.65032
[2] Duff, I. S., Reid, J. K.: A comparison of sparsity orderings for obtaining a pivotal sequence in Gaussian elimination. (To appear in J. IMA, 1974a.) · Zbl 0308.65021
[3] Duff, I. S., Reid, J. K.: A comparison of some methods for the solution of sparse overdetermined systems of linear equations. (To appear in J. IMA. 1974b.) · Zbl 0329.65026
[4] Duff, I. S., Reid, J. K.: On the reduction of sparse matrices to condensed forms by similarity transformations. (To appear in J. IMA, 1974c.) · Zbl 0299.15006
[5] Gentleman, W. M.: Least squares computations by Givens transformations without square roots. J. IMA12, 329–336 (1973). · Zbl 0289.65020
[6] Golub, G. H.: Numerical methods for solving linear least squares problems. Num. Math.7, 206–216 (1965). · Zbl 0142.11502 · doi:10.1007/BF01436075
[7] Markowitz, H. M.: The elimination form of the inverse and its application to linear programming. Management Science3, 255–269 (1957). · Zbl 0995.90592 · doi:10.1287/mnsc.3.3.255
[8] Wilkinson, J. H.: The Algebraic Eigenvalue Problem. Oxford University Press. 1965. · Zbl 0258.65037
[9] Willoughby, R. A.: Sparse matrix algorithms and their relation to problem classes and computer architecture. In: Large Sparse Sets of Linear Equations (Reid, J. K., ed.). Academic Press 1971.
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