Geodesic
Direct methods for solving large sparse equations based on the block two by two decomposition of the matrix
Matematičeskoe modelirovanie, Tome 5 (1993) no. 2, pp. 66-81 Cet article a éte moissonné depuis la source Math-Net.Ru

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Several algorithms for reordering sparse symmetric positive definite matrix to a block two by two form are considered; a task of finding a permutation such that filling is at minimum in a block $(1,1)$ and is located mainly in blocks $(2,1)$, $(2,2)$ is posed. In this respect two algorithms from widely known sparse matrix package SPARSPAK are analyzed: QMD – a Quotient Minimum Degree and ND – nested dissection algorithms; a new one is proposed which is called $\mathrm{BND}+\mathrm{qmd}$ – Balanced ND with internal (influencing block $(1,1)$) qmd-ordering. The results of numerical experiments for a set of grid problems containing 10000–25000 unknown values are presented. These results show the usage of implicit solution scheme may provide up to 25–30% reduction of primary storage without visible increasing the number of operations required to solve triangular system. 
@article{MM_1993_5_2_a5,
     author = {A. B. Kycherov and E. J. Oleinik},
     title = {Direct methods for solving large sparse equations based on the block two by two decomposition of the matrix},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {66--81},
     year = {1993},
     volume = {5},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1993_5_2_a5/}
}
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A. B. Kycherov; E. J. Oleinik. Direct methods for solving large sparse equations based on the block two by two decomposition of the matrix. Matematičeskoe modelirovanie, Tome 5 (1993) no. 2, pp. 66-81. http://geodesic.mathdoc.fr/item/MM_1993_5_2_a5/