Alex Pothen - Publications

	CS Dept. Bio Projects Publications Presentations Software Courses Outreach Group Contact		Publications Overview Papers and News Articles Graph Coloring and Scientific Computation Graph Matching and Scientific Computation Graph Partitioning, Ordering, and Related Problems Parallel and Sequential Sparse Matrix Computations Computational Systems Biology and Bioinformatics Miscellaneous Topics Overview Papers and News Articles E.G. Boman, D. Bozdag, U. Catalyurek, K. Devine, A.H. Gebremedhin, P. Hovland and A. Pothen, Combinatorial Algorithms for Computational Science and Engineering , Journal of Physics: Conference Series 125 (2008) 012071, 5 pp. SciDAC 2008. A. Pothen, A.H. Gebremedhin, F. Dobrian, E.G. Boman, K.D. Devine, B.A. Hendrickson, P. Hovland, B. Norris, J. Utke, U. Catalyurek, M.M. Strout, Combinatorial Algorithms for Petascale Science , SciDAC Review, Issue 5, pp 26-35, Fall 2007. E.G. Boman, D. Bozdag, U.V. Catalyurek, K.D. Devine, A.H. Gebremedhin, P.D. Hovland, A. Pothen, and M.M. Strout, Enabling high performance computational science through combinatorial algorithms , Proceedings of SciDAC 2007, Journal of Physics: Conference Series 78 (2007) 012058. B. Hendrickson, and A. Pothen, Combinatorial Scientific Computing: The enabling power of discrete algorithms in computational science , Proceedings of the 7th International Meeting on High Performance Computing for Computational Science (VECPAR'06), Lecture Notes in Computer Science, Springer Verlag, 21 pp., 2006. (Invited paper) S. Bhomwick, E.G. Boman, K. Devine, A.H. Gebremedhin, B. Hendrickson, P. Hovland, T. Munson and A. Pothen, Combinatorial Algorithms Enabling Computational Science: Tales from the Front , Journal of Physics: Conference Series 46 (2006), 453-457, SciDAC 2006. A. Pothen, Dedication to Alan George , Electronic Transactions on Numerical Analysis, Special Volume on Combinatorial Scientific Computing, 21, pp. vii--xviii, Dec. 2005. Graph Coloring and Scientific Computation A.H. Gebremedhin, A. Pothen, A. Tarafdar, and A. Walther, Efficient computation of sparse Hessians using coloring and Automatic Differentiation , INFORMS Journal on Computing, 28 pp., 2008 (to appear). A.H. Gebremedhin, A. Pothen, and A. Walther, Exploiting Sparsity in Jacobian Computation via Coloring and Automatic Differentiation: a Case Study in a Simulated Moving Bed process , In C. Bischof et al. (Eds.): Proceeding of AD2008, The 5th Int'l Conference on AD, Lecture Notes in Computational Science and Engineering 64, pp. 339-349, 2008, Springer. A. Gebremedhin, A. Tarafdar, F. Manne and A. Pothen, New Acyclic and Star Coloring Algorithms with Applications to Hessian Computation , SIAM Journal on Scientific Computing, Vol 29, No 3, pp 1042--1072, 2007. Graph Matching and Scientific Computation A. Pinar, E. Chow and A. Pothen, Combinatorial Algorithms for Computing Column Space Bases that have Sparse Inverses , Electronic Transactions on Numerical Analysis, 22, pp. 122--145, 2006. A. Pothen, Predicting the structure of sparse orthogonal factors (compressed postscript file), Lin. Alg. Applic., 194 (1993), 183--204. Graph Partitioning, Ordering, and Related Problems Pinar Heggernes, Stan Eisenstat, Gary Kumfert and A. Pothen, The computational complexity of the minimum degree algorithm , Proceedings of the Norwegian Conference on Computer Science NIK, 2002. D. Hysom and A. Pothen, A scalable parallel algorithm for incomplete factor preconditioning , SIAM Journal on Scientific Computing, 22(6), 2194--2215, 2001. D. Hysom and A. Pothen, Efficient Parallel Computation of ILU(k) Preconditioners , Proceedings of Supercomputing '99 (CDROM), 1999. G. Kumfert and A. Pothen, An object-oriented collection of minimum degree algorithms: design, implementation, and experiences , In Computing in Object-oriented Parallel Environments, Lecture Notes in Computer Science 1505, D.~Caromel et al (eds.), pp. 95--106, Springer Verlag, 1998. (Proceedings of the Second International Symposium on Computing in Object-oriented Parallel Environments, Santa Fe, 1998.) G. Kumfert and A. Pothen, Two improved algorithms for envelope and wavefront reduction , invited paper, BIT, 37(3), 559--590, 1997. A. George and A. Pothen, An analysis of spectral envelope-reduction via quadratic assignment problems , SIAM Journal of Matrix Analysis and its Applications, 18(3), pp. 706--732, 1997. A. Pothen, Graph partitioning algorithms with applications to scientific computing , In Parallel Numerical Algorithms, D. E. Keyes, A. H. Sameh and V. Venkatakrishnan (eds.), Kluwer Academic Press, 1996. (46 pages) S. T. Barnard, A. Pothen and H. D. Simon, A spectral algorithm for envelope reduction of sparse matrices , Numerical Linear Algebra with Applications, 2, pp. 317--334, 1995. B. W. Peyton, A. Pothen and X. Yuan, A clique tree algorithm for partitioning a chordal graph into transitive subgraphs , Linear Algebra and its Applications, 223/224, pp. 553--588, 1995. B. W. Peyton, A. Pothen and X. Yuan, A clique tree algorithm for partitioning a chordal graph into transitive subgraphs (compressed postscript file), Linear Algebra and its Applications, 192, pp. 329--354, 1993. F. L. Alvarado, A. Pothen and R. S. Schreiber, Highly parallel sparse triangular solution (compressed postscript file), In Graph Theory and Sparse Matrix Computation, IMA vol. in Appl. Math., 56, 141--158, 1993. (Springer Verlag) Parallel and Sequential Sparse Matrix Computations F. Dobrian and A. Pothen, Oblio: Design and Performance , in State of the Art in Scientific Computing, J. Dongarra, K. Madsen and J. Wasniewski (eds.), Lecture Notes in Computer Science, 3732, pp. 758--767, 2005. A. Pothen and S. Toledo, Elimination structures in scientific computing, In Handbook on Data Structures and Applications , Chapter 59, 29 pp., Dinesh Mehta and Sartaj Sahni, editors, Chapman and Hall /CRC, 2004. Florin Dobrian and A. Pothen, A comparison between three external memory algorithms for factoring sparse matrices , Proceedings of the SIAM Conference on Applied Linear Algebra, 11 pp, July 2003. David Hysom and A. Pothen, Level-based Incomplete LU factorization: Graph Model and Algorithms , Tech Report UCRL-JC-150789, Lawrence Livermore National Labs, 19 pp., Nov 2002. Pinar Heggernes, Stan Eisenstat, Gary Kumfert and A. Pothen, The computational complexity of the minimum degree algorithm , Proceedings of the Norwegian Conference on Computer Science NIK, 2002. Florin Dobrian and A. Pothen, The Design of I/O efficient Sparse Direct Solvers , Proceedings of Supercomputing 2001, IEEE and ACM. Florin Dobrian, External memory algorithms for factoring sparse matrices , PhD Thesis, Old Dominion University, Dec. 2001. David Hysom, New parallel and sequential algorithms for incomplete factor preconditioners , PhD Thesis, Old Dominion University, Dec. 2001. D. Hysom and A. Pothen, A scalable parallel algorithm for incomplete factor preconditioning , SIAM Journal on Scientific Computing, 22(6), 2194--2215, 2001. F. Dobrian and A. Pothen, Oblio: a sparse direct solver library for serial and parallel computations , Technical Report describing the OBLIO software library, 2000. F. Dobrian, G. Kumfert and A. Pothen, The Design of Sparse Direct Solvers using Object-Oriented Techniques , In Modern Software Tools in Scientific Computing, A. M. Bruaset, H. P. Langtangen and E. Quak (eds.), pp. 89--131, Springer-Verlag, 2000. Gary Karl Kumfert, An object-oriented algorithmic laboratory for ordering sparse matrices , PhD Thesis, Old Dominion University, Dec. 2000. D. Hysom and A. Pothen, Efficient Parallel Computation of ILU(k) Preconditioners , Proceedings of Supercomputing '99 (CDROM), 1999. G. Kumfert and A. Pothen, An object-oriented collection of minimum degree algorithms: design, implementation, and experiences , In Computing in Object-oriented Parallel Environments, Lecture Notes in Computer Science 1505, D.~Caromel et al (eds.), pp. 95--106, Springer Verlag, 1998. (Proceedings of the Second International Symposium on Computing in Object-oriented Parallel Environments, Santa Fe, 1998.) Florin Dobrian, Gary Kumfert, and Alex Pothen, Object-Oriented Design for Sparse Direct Solvers , In Computing in Object-oriented Parallel Environments, Lecture Notes in Computer Science 1505, D.~Caromel et al (eds.), pp. 207--214, Springer Verlag, 1998. (Proceedings of the Second International Symposium on Computing in Object-oriented Parallel Environments, Santa Fe, 1998.) G. Kumfert and A. Pothen, Two improved algorithms for envelope and wavefront reduction , invited paper, BIT, 37(3), 559--590, 1997. A. George and A. Pothen, An analysis of spectral envelope-reduction via quadratic assignment problems , SIAM Journal of Matrix Analysis and its Applications, 18(3), pp. 706--732, 1997. S. T. Barnard, A. Pothen and H. D. Simon, A spectral algorithm for envelope reduction of sparse matrices , Numerical Linear Algebra with Applications, 2, pp. 317--334, 1995. F. L. Alvarado, A. Pothen and R. S. Schreiber, Highly parallel sparse triangular solution (compressed postscript file), In Graph Theory and Sparse Matrix Computation, IMA vol. in Appl. Math., 56, 141--158, 1993. (Springer Verlag) A. Pothen, Predicting the structure of sparse orthogonal factors (compressed postscript file), Lin. Alg. Applic., 194 (1993), 183--204. A. Pothen and C.Sun, A mapping algorithm for parallel sparse Cholesky factorization (compressed postscript file), SIAM J. Sci. Computing, 14 (1993), 1253--1257. Computational Systems Biology and Bioinformatics Emad Ramadan, Michael Ward, Xin Guo, Sarah Durkin, Adam Sawyer, Marcelo Viela, Chris Osgood, Alex Pothen and O. John Semmes, Physical and in silico approaches identify DNA-PK in a Tax DNA-damage response interactome, Retrovirology, 5:92, 13 pages, 2008 E. Ramadan, C. Osgood, and A. Pothen, The architecture of a proteomic network in the yeast , Proceedings of CompLife2005, Lecture Notes in Bioinformatics, Vol. 3695, pp. 265--276, 2005. Badr Al-Mutairy, Jolan E. Walter, Alex Pothen and Douglas K. Mitchell, Genomic mapping of genome-linked viral protein (VPG) and helicase of astroviruses , Virus Genes, 31 (1), pp. 21--30, 2005. M. Wagner, D. Naik, A. Pothen et al., Computational protein biomarker prediction: a case study for prostate cancer , BMC Bioinformatics, 5, 26 pp., March 2004. Emad Ramadan, Arijit Tarafdar, and A. Pothen, A hypergraph model for the yeast protein complex network , Proceedings of the IEEE Workshop on High Performance Computational Biology, April 2004. (Presented at the HICOMB Workshop, Santa Fe, NM, IEEE) Michael Wagner, Dayanand Naik, and A. Pothen, Protocols for disease classification from mass spectrometry data , Proteomics, Vol 3 (9), pp. 1692--1698, Sep 2003. (Presented at the First Annual Proteomics Datamining Conference at the Duke Medical School) Miscellaneous Topics I. Stoica and A. Pothen, A robust and flexible microeconomic scheduler for parallel computers , Preprint, Dec 1996. Proceedings of Third International Conference on High Performance Computing, Thiruvananthapuram, India. I. Stoica, H. Abdel-Wahab, and A.Pothen, A microeconomic scheduler for parallel computers , In Load-balancing and Job Scheduling for Parallel Computers, D. G. Feitelson and L. Rudolph (eds.), Lecture Notes in Computer Science, Vol. 949, Springer-Verlag, pp. 200--218, 1995. R.A.Brualdi, A. Pothen and S. Friedland, The sparse basis problem and multilinear algebra (compressed postscript file), SIAM J. Matrix Anal. Applic., 16, pp. 1--20, 1995. N.J. Higham and A.Pothen, Stability of the partitioned inverse method for parallel solution of sparse triangular systems (compressed postscript file), SIAM J. Sci. Computing, 15, 139--148, 1994.

Overview Papers and News Articles

  E.G. Boman, D. Bozdag, U. Catalyurek, K. Devine, A.H. Gebremedhin, P. Hovland and A. Pothen, Combinatorial Algorithms for Computational Science and Engineering , Journal of Physics: Conference Series 125 (2008) 012071, 5 pp. SciDAC 2008.

  A. Pothen, A.H. Gebremedhin, F. Dobrian, E.G. Boman, K.D. Devine, B.A. Hendrickson, P. Hovland, B. Norris, J. Utke, U. Catalyurek, M.M. Strout, Combinatorial Algorithms for Petascale Science , SciDAC Review, Issue 5, pp 26-35, Fall 2007.

  E.G. Boman, D. Bozdag, U.V. Catalyurek, K.D. Devine, A.H. Gebremedhin, P.D. Hovland, A. Pothen, and M.M. Strout, Enabling high performance computational science through combinatorial algorithms , Proceedings of SciDAC 2007, Journal of Physics: Conference Series 78 (2007) 012058.

  B. Hendrickson, and A. Pothen, Combinatorial Scientific Computing: The enabling power of discrete algorithms in computational science , Proceedings of the 7th International Meeting on High Performance Computing for Computational Science (VECPAR'06), Lecture Notes in Computer Science, Springer Verlag, 21 pp., 2006. (Invited paper)

  S. Bhomwick, E.G. Boman, K. Devine, A.H. Gebremedhin, B. Hendrickson, P. Hovland, T. Munson and A. Pothen, Combinatorial Algorithms Enabling Computational Science: Tales from the Front , Journal of Physics: Conference Series 46 (2006), 453-457, SciDAC 2006.

  A. Pothen, Dedication to Alan George , Electronic Transactions on Numerical Analysis, Special Volume on Combinatorial Scientific Computing, 21, pp. vii--xviii, Dec. 2005.

Graph Coloring and Scientific Computation

  A.H. Gebremedhin, A. Pothen, A. Tarafdar, and A. Walther, Efficient computation of sparse Hessians using coloring and Automatic Differentiation , INFORMS Journal on Computing, 28 pp., 2008 (to appear).

  A.H. Gebremedhin, A. Pothen, and A. Walther, Exploiting Sparsity in Jacobian Computation via Coloring and Automatic Differentiation: a Case Study in a Simulated Moving Bed process , In C. Bischof et al. (Eds.): Proceeding of AD2008, The 5th Int'l Conference on AD, Lecture Notes in Computational Science and Engineering 64, pp. 339-349, 2008, Springer.

  A. Gebremedhin, A. Tarafdar, F. Manne and A. Pothen, New Acyclic and Star Coloring Algorithms with Applications to Hessian Computation , SIAM Journal on Scientific Computing, Vol 29, No 3, pp 1042--1072, 2007.

Graph Matching and Scientific Computation

A. Pinar, E. Chow and A. Pothen, Combinatorial Algorithms for Computing Column Space Bases that have Sparse Inverses , Electronic Transactions on Numerical Analysis, 22, pp. 122--145, 2006.

A. Pothen, Predicting the structure of sparse orthogonal factors (compressed postscript file), Lin. Alg. Applic., 194 (1993), 183--204.

Graph Partitioning, Ordering, and Related Problems

  Pinar Heggernes, Stan Eisenstat, Gary Kumfert and A. Pothen, The computational complexity of the minimum degree algorithm , Proceedings of the Norwegian Conference on Computer Science NIK, 2002.

  D. Hysom and A. Pothen, A scalable parallel algorithm for incomplete factor preconditioning , SIAM Journal on Scientific Computing, 22(6), 2194--2215, 2001.

  D. Hysom and A. Pothen, Efficient Parallel Computation of ILU(k) Preconditioners , Proceedings of Supercomputing '99 (CDROM), 1999.

  G. Kumfert and A. Pothen, An object-oriented collection of minimum degree algorithms: design, implementation, and experiences , In Computing in Object-oriented Parallel Environments, Lecture Notes in Computer Science 1505, D.~Caromel et al (eds.), pp. 95--106, Springer Verlag, 1998. (Proceedings of the Second International Symposium on Computing in Object-oriented Parallel Environments, Santa Fe, 1998.)

  G. Kumfert and A. Pothen, Two improved algorithms for envelope and wavefront reduction , invited paper, BIT, 37(3), 559--590, 1997.

  A. George and A. Pothen, An analysis of spectral envelope-reduction via quadratic assignment problems , SIAM Journal of Matrix Analysis and its Applications, 18(3), pp. 706--732, 1997.

  A. Pothen, Graph partitioning algorithms with applications to scientific computing , In Parallel Numerical Algorithms, D. E. Keyes, A. H. Sameh and V. Venkatakrishnan (eds.), Kluwer Academic Press, 1996. (46 pages)

  S. T. Barnard, A. Pothen and H. D. Simon, A spectral algorithm for envelope reduction of sparse matrices , Numerical Linear Algebra with Applications, 2, pp. 317--334, 1995.

  B. W. Peyton, A. Pothen and X. Yuan, A clique tree algorithm for partitioning a chordal graph into transitive subgraphs , Linear Algebra and its Applications, 223/224, pp. 553--588, 1995.

  B. W. Peyton, A. Pothen and X. Yuan, A clique tree algorithm for partitioning a chordal graph into transitive subgraphs (compressed postscript file), Linear Algebra and its Applications, 192, pp. 329--354, 1993.

  F. L. Alvarado, A. Pothen and R. S. Schreiber, Highly parallel sparse triangular solution (compressed postscript file), In Graph Theory and Sparse Matrix Computation, IMA vol. in Appl. Math., 56, 141--158, 1993. (Springer Verlag)

Parallel and Sequential Sparse Matrix Computations

  F. Dobrian and A. Pothen, Oblio: Design and Performance , in State of the Art in Scientific Computing, J. Dongarra, K. Madsen and J. Wasniewski (eds.), Lecture Notes in Computer Science, 3732, pp. 758--767, 2005.

  A. Pothen and S. Toledo, Elimination structures in scientific computing, In Handbook on Data Structures and Applications , Chapter 59, 29 pp., Dinesh Mehta and Sartaj Sahni, editors, Chapman and Hall /CRC, 2004.

  Florin Dobrian and A. Pothen, A comparison between three external memory algorithms for factoring sparse matrices , Proceedings of the SIAM Conference on Applied Linear Algebra, 11 pp, July 2003.

  David Hysom and A. Pothen, Level-based Incomplete LU factorization: Graph Model and Algorithms , Tech Report UCRL-JC-150789, Lawrence Livermore National Labs, 19 pp., Nov 2002.

  Pinar Heggernes, Stan Eisenstat, Gary Kumfert and A. Pothen, The computational complexity of the minimum degree algorithm , Proceedings of the Norwegian Conference on Computer Science NIK, 2002.

  Florin Dobrian and A. Pothen, The Design of I/O efficient Sparse Direct Solvers , Proceedings of Supercomputing 2001, IEEE and ACM.

  Florin Dobrian, External memory algorithms for factoring sparse matrices , PhD Thesis, Old Dominion University, Dec. 2001.

  David Hysom, New parallel and sequential algorithms for incomplete factor preconditioners , PhD Thesis, Old Dominion University, Dec. 2001.

  D. Hysom and A. Pothen, A scalable parallel algorithm for incomplete factor preconditioning , SIAM Journal on Scientific Computing, 22(6), 2194--2215, 2001.

  F. Dobrian and A. Pothen, Oblio: a sparse direct solver library for serial and parallel computations , Technical Report describing the OBLIO software library, 2000.

  F. Dobrian, G. Kumfert and A. Pothen, The Design of Sparse Direct Solvers using Object-Oriented Techniques , In Modern Software Tools in Scientific Computing, A. M. Bruaset, H. P. Langtangen and E. Quak (eds.), pp. 89--131, Springer-Verlag, 2000.

  Gary Karl Kumfert, An object-oriented algorithmic laboratory for ordering sparse matrices , PhD Thesis, Old Dominion University, Dec. 2000.

  D. Hysom and A. Pothen, Efficient Parallel Computation of ILU(k) Preconditioners , Proceedings of Supercomputing '99 (CDROM), 1999.

  G. Kumfert and A. Pothen, An object-oriented collection of minimum degree algorithms: design, implementation, and experiences , In Computing in Object-oriented Parallel Environments, Lecture Notes in Computer Science 1505, D.~Caromel et al (eds.), pp. 95--106, Springer Verlag, 1998. (Proceedings of the Second International Symposium on Computing in Object-oriented Parallel Environments, Santa Fe, 1998.)

  Florin Dobrian, Gary Kumfert, and Alex Pothen, Object-Oriented Design for Sparse Direct Solvers , In Computing in Object-oriented Parallel Environments, Lecture Notes in Computer Science 1505, D.~Caromel et al (eds.), pp. 207--214, Springer Verlag, 1998. (Proceedings of the Second International Symposium on Computing in Object-oriented Parallel Environments, Santa Fe, 1998.)

  G. Kumfert and A. Pothen, Two improved algorithms for envelope and wavefront reduction , invited paper, BIT, 37(3), 559--590, 1997.

  A. George and A. Pothen, An analysis of spectral envelope-reduction via quadratic assignment problems , SIAM Journal of Matrix Analysis and its Applications, 18(3), pp. 706--732, 1997.

  S. T. Barnard, A. Pothen and H. D. Simon, A spectral algorithm for envelope reduction of sparse matrices , Numerical Linear Algebra with Applications, 2, pp. 317--334, 1995.

  F. L. Alvarado, A. Pothen and R. S. Schreiber, Highly parallel sparse triangular solution (compressed postscript file), In Graph Theory and Sparse Matrix Computation, IMA vol. in Appl. Math., 56, 141--158, 1993. (Springer Verlag)

  A. Pothen, Predicting the structure of sparse orthogonal factors (compressed postscript file), Lin. Alg. Applic., 194 (1993), 183--204.

  A. Pothen and C.Sun, A mapping algorithm for parallel sparse Cholesky factorization (compressed postscript file), SIAM J. Sci. Computing, 14 (1993), 1253--1257.

Computational Systems Biology and Bioinformatics

  Emad Ramadan, Michael Ward, Xin Guo, Sarah Durkin, Adam Sawyer, Marcelo Viela, Chris Osgood, Alex Pothen and O. John Semmes, Physical and in silico approaches identify DNA-PK in a Tax DNA-damage response interactome, Retrovirology, 5:92, 13 pages, 2008

  E. Ramadan, C. Osgood, and A. Pothen, The architecture of a proteomic network in the yeast , Proceedings of CompLife2005, Lecture Notes in Bioinformatics, Vol. 3695, pp. 265--276, 2005.

  Badr Al-Mutairy, Jolan E. Walter, Alex Pothen and Douglas K. Mitchell, Genomic mapping of genome-linked viral protein (VPG) and helicase of astroviruses , Virus Genes, 31 (1), pp. 21--30, 2005.

  M. Wagner, D. Naik, A. Pothen et al., Computational protein biomarker prediction: a case study for prostate cancer , BMC Bioinformatics, 5, 26 pp., March 2004.

  Emad Ramadan, Arijit Tarafdar, and A. Pothen, A hypergraph model for the yeast protein complex network , Proceedings of the IEEE Workshop on High Performance Computational Biology, April 2004. (Presented at the HICOMB Workshop, Santa Fe, NM, IEEE)

  Michael Wagner, Dayanand Naik, and A. Pothen, Protocols for disease classification from mass spectrometry data , Proteomics, Vol 3 (9), pp. 1692--1698, Sep 2003. (Presented at the First Annual Proteomics Datamining Conference at the Duke Medical School)

Miscellaneous Topics

  I. Stoica and A. Pothen, A robust and flexible microeconomic scheduler for parallel computers , Preprint, Dec 1996. Proceedings of Third International Conference on High Performance Computing, Thiruvananthapuram, India.

  I. Stoica, H. Abdel-Wahab, and A.Pothen, A microeconomic scheduler for parallel computers , In Load-balancing and Job Scheduling for Parallel Computers, D. G. Feitelson and L. Rudolph (eds.), Lecture Notes in Computer Science, Vol. 949, Springer-Verlag, pp. 200--218, 1995.

  R.A.Brualdi, A. Pothen and S. Friedland, The sparse basis problem and multilinear algebra (compressed postscript file), SIAM J. Matrix Anal. Applic., 16, pp. 1--20, 1995.

  N.J. Higham and A.Pothen, Stability of the partitioned inverse method for parallel solution of sparse triangular systems (compressed postscript file), SIAM J. Sci. Computing, 15, 139--148, 1994.