Permasalahan Kombinatorial Dalam Menyelesaikan Sistem Linier
DAFTAR PUSTAKA
Amestoy, P. R., Davis, T. A. dan Duff, I. S. (1996). An approximate minimum degree ordering algorithm. SIAM Journal on Matrix Analysis and Applications,
Volume 17, 886–905.
Amestoy P. R., Duff, I. S. dan L’Excellent, J. Y. (2000). Multifrontal parallel distributed symmetric and unsymmetric solvers. Computer methods in applied
mechanics and engineering, Volume 184, 501–520.
Ashcraft C. dan Liu, J. W. H. (1998). Robust ordering of sparse matrices using
multisection. SIAM Journal on Matrix Analysis and Applications, Volume
19, 816–832.
Bhat, M. V., W. G. Habashi, Liu, J. W. H., Nguyen, V. N. dan Peeters, M. F.
(1993). A note on nested dissection for rectangular grids. SIAM Journal on
Matrix Analysis and Applications, Volume 14, 253–258.
Bollhofer, M. dan Schenk, O. (2004). Combinatorial aspects in sparse elimination
methods. GAMM Mitteilungen, Volume 29, 1111–1130
Brualdi R. A. dan Cvetkovic D. M. (2009). A Combinatorial Approach to Matrix
Theory and its Applications. Chapman & Hall/CRC Press, Boca Raton.
Brualdi R. A. dan Ryser H. J. (1991). Combinatorial Matrix Theory. Cambridge
University Press, Cambridge.
Burkard, R., Dell’Amico, M. dan Martello, S. (2009). Assignment Problems. SIAM,
Philadelphia, PA, USA.
Chen, T. (2001). Preconditioning Sparse Matrices for Computing Eigenvalues and
Solving Linear Systems of Equations. Dissertation Doctor Of Philosophy.
University of California, Berkeley.
Cuthill, E. dan McKee, J. (1969). Reducing the bandwidth of sparse symmetric
matrices. Proceedings of the 24th national conference, New York, NY, USA,
ACM, 157–172.
Dongarra, J. J., Du Croz, J., Duff, I. S. dan Hammarling, S. (1990). A set of Level
3 Basic Linear Algebra Subprograms. ACM Transactions on Mathematical
Software, Volume 16, 1–17.
Duff, I. S. dan Koster, J. (2001). On algorithms for permuting large entries to the
diagonal of a sparse matrix. SIAM Journal on Matrix Analysis and Applications, Volume 22, 973–996.
Duff,
I. S. (1982). Full matrix techniques in sparse Gaussian elimination.Proceedings of 1981 Dundee Biennal Conference on Numerical Analysis,
G. A. Watson, ed., Volume 912 of Lecture Notes in Mathematics, 71–84.
Duff, I. S. dan Ucar, B. (2009). Combinatorial problems in solving linear
systems. Technical Report No. TR/PA/09/60, CERFACS, available at
http://www.cerfacs.fr/algor/reports/. France.
41
Universitas Sumatera Utara
42
Fredman, M. L. dan Tarjan, R. E. (1987). Fibonacci heaps and their uses in improved network optimization algorithms. J. AC. Volume 34, 596–615.
Garey, M. R. dan Johnson, D. S. (1991). Computers and intractability: A guide to
the theory of NP-completeness. W.H. Freeman. New York.
Gilbert, J. R. dan Tarjan, R. E. (1987). The analysis of a nested dissection algorithm. Numerische Mathematic, Volume 50, 377–404.
George A. J. (1971). Computer implementation of the finite element method, PhD
thesis. Stanford University, Stanford, CA, USA.
George, A. (1973). Nested dissection of a regular inite element mesh. SIAM J.
Numer. Anal., Volume 10 , 345–363.
George, A. dan Liu, J. W. H. (1978). An automatic nested dissection algorithm for
irregular initeelement problems. SIAM J. Numer. Anal., Volume 15 , 1053–
1069.
George, A. dan Liu, J. W. H. (1989). The evolution of the minimum degree ordeing
algoithm. SIAM Rev., Volume 31.
George, A. dan Ng, E. (1985). An implementation of Gaussian Elimination with
partial pivoting for sparse systems. SIAM J. Sci. Stat. Comput., Volume 6(2),
390-409,
Gould, N. I. M., Yifan Hu, dan Jennifer A. Scott. (2005). A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations. Report RAL-TR-2005-005, Computational Sciences
and Engineering Department, Rutherford Appleton Laboratory, Oxon, OX11
0QX, England.
Heath, M. T., Ng, E. dan Peyton, B. W. (1991). Parallel algorithms for sparse
linear systems. SIAM Review, Volume 33, 420–460.
Heggernes, P., Eisenstat, S. C., Kumfert, G. dan Pothen, A. (2001). The computational complexity of the minimum degree algorithm, Proceedings of NIK
2001—14th Norwegian Computer Science Conference, Tromso, Norway, 98–
109.
Hendrickson, B. dan Pothen, A. (2007). Combinatorial scientific computing: The
enabling power of discrete algorithms in computational science, High Performance Computing for Computational Science—VECPAR 2006, M. Dayde,
M. L. M. Palma, L. G. A. Coutinho, E. Pacitti, and J. C. Lopes, eds., Volume 4395 of Lecture Notes in Computer Science, 260–280.
Lipton, R. J., Rose, D. J. dan Tarjan, R. E. (1979). Generalized nested dissection.
SIAM Journal on Numerical Analysis,Volume 16, 346–358
Lipton, R. J. dan Tarjan, R. E. (1979). A separator theorem for planar graphs.
SIAM Journal on Applied Mathematics, Volume 36, 177–189.
Liu, J. W. H. dan Sherman, A. H. (1976). Comparative analysis of the CuthillMcKee and the Reverse Cuthill-McKee ordering algorithms for sparse matrices. SIAM Journal on Numerical Analysis, Volume 13, 198–213.
Universitas Sumatera Utara
43
Liu, J. W. H. (1986). On the storage requirement in the out-of-core multifrontal
method for sparse factor- ization. ACM Transactions on Mathematical Software, Volume 12 , 249–264.
Liu, J. W. H. (1989). The minimum degree ordering with constraints. SIAM Journal on Scientific and Statistical Computing, Volume 10, 1136–1145.
Liu, J. W. H. (1992).The multifrontal method for sparse matrix solution: Theory
and practice. SIAM Review, Volume 34, 82–109.
Olschowka, M. dan Neumaier, A. (1996). A new pivoting strategy for Gaussian
elimination. Linear Algebra and Its Applications, Volume 240, 131–151.
Reid, J. K. dan Scott, J. A. (2006). An out-of-core sparse Cholesky solver, Tech.
Report RAL-TR-2006-013, Computational Sciences and Engineering Department, Rutherford Appleton Laboratory, Oxon, OX11 0QX, England.
Saad, Y. (2003). Iterative Methods for Sparse Linear Systems (Second Edition.SIAM, Amerika.
Tarjan, R. E. (1972). Depth-first search and linear graph algorithms. SIAM Journal
on Computing, Volume 1, 146–160.
Warsito, A. (2009). Fisika Komputasi. FST Universitas Nusa Cendana, NTT.
Yannakakis, M. (1981). Computing the minimum ill-in is NP-complete, SIAM J.
Algebraic Discrete Methods, Volume 2, 77–79.
Universitas Sumatera Utara
Amestoy, P. R., Davis, T. A. dan Duff, I. S. (1996). An approximate minimum degree ordering algorithm. SIAM Journal on Matrix Analysis and Applications,
Volume 17, 886–905.
Amestoy P. R., Duff, I. S. dan L’Excellent, J. Y. (2000). Multifrontal parallel distributed symmetric and unsymmetric solvers. Computer methods in applied
mechanics and engineering, Volume 184, 501–520.
Ashcraft C. dan Liu, J. W. H. (1998). Robust ordering of sparse matrices using
multisection. SIAM Journal on Matrix Analysis and Applications, Volume
19, 816–832.
Bhat, M. V., W. G. Habashi, Liu, J. W. H., Nguyen, V. N. dan Peeters, M. F.
(1993). A note on nested dissection for rectangular grids. SIAM Journal on
Matrix Analysis and Applications, Volume 14, 253–258.
Bollhofer, M. dan Schenk, O. (2004). Combinatorial aspects in sparse elimination
methods. GAMM Mitteilungen, Volume 29, 1111–1130
Brualdi R. A. dan Cvetkovic D. M. (2009). A Combinatorial Approach to Matrix
Theory and its Applications. Chapman & Hall/CRC Press, Boca Raton.
Brualdi R. A. dan Ryser H. J. (1991). Combinatorial Matrix Theory. Cambridge
University Press, Cambridge.
Burkard, R., Dell’Amico, M. dan Martello, S. (2009). Assignment Problems. SIAM,
Philadelphia, PA, USA.
Chen, T. (2001). Preconditioning Sparse Matrices for Computing Eigenvalues and
Solving Linear Systems of Equations. Dissertation Doctor Of Philosophy.
University of California, Berkeley.
Cuthill, E. dan McKee, J. (1969). Reducing the bandwidth of sparse symmetric
matrices. Proceedings of the 24th national conference, New York, NY, USA,
ACM, 157–172.
Dongarra, J. J., Du Croz, J., Duff, I. S. dan Hammarling, S. (1990). A set of Level
3 Basic Linear Algebra Subprograms. ACM Transactions on Mathematical
Software, Volume 16, 1–17.
Duff, I. S. dan Koster, J. (2001). On algorithms for permuting large entries to the
diagonal of a sparse matrix. SIAM Journal on Matrix Analysis and Applications, Volume 22, 973–996.
Duff,
I. S. (1982). Full matrix techniques in sparse Gaussian elimination.Proceedings of 1981 Dundee Biennal Conference on Numerical Analysis,
G. A. Watson, ed., Volume 912 of Lecture Notes in Mathematics, 71–84.
Duff, I. S. dan Ucar, B. (2009). Combinatorial problems in solving linear
systems. Technical Report No. TR/PA/09/60, CERFACS, available at
http://www.cerfacs.fr/algor/reports/. France.
41
Universitas Sumatera Utara
42
Fredman, M. L. dan Tarjan, R. E. (1987). Fibonacci heaps and their uses in improved network optimization algorithms. J. AC. Volume 34, 596–615.
Garey, M. R. dan Johnson, D. S. (1991). Computers and intractability: A guide to
the theory of NP-completeness. W.H. Freeman. New York.
Gilbert, J. R. dan Tarjan, R. E. (1987). The analysis of a nested dissection algorithm. Numerische Mathematic, Volume 50, 377–404.
George A. J. (1971). Computer implementation of the finite element method, PhD
thesis. Stanford University, Stanford, CA, USA.
George, A. (1973). Nested dissection of a regular inite element mesh. SIAM J.
Numer. Anal., Volume 10 , 345–363.
George, A. dan Liu, J. W. H. (1978). An automatic nested dissection algorithm for
irregular initeelement problems. SIAM J. Numer. Anal., Volume 15 , 1053–
1069.
George, A. dan Liu, J. W. H. (1989). The evolution of the minimum degree ordeing
algoithm. SIAM Rev., Volume 31.
George, A. dan Ng, E. (1985). An implementation of Gaussian Elimination with
partial pivoting for sparse systems. SIAM J. Sci. Stat. Comput., Volume 6(2),
390-409,
Gould, N. I. M., Yifan Hu, dan Jennifer A. Scott. (2005). A numerical evaluation of sparse direct solvers for the solution of large sparse, symmetric linear systems of equations. Report RAL-TR-2005-005, Computational Sciences
and Engineering Department, Rutherford Appleton Laboratory, Oxon, OX11
0QX, England.
Heath, M. T., Ng, E. dan Peyton, B. W. (1991). Parallel algorithms for sparse
linear systems. SIAM Review, Volume 33, 420–460.
Heggernes, P., Eisenstat, S. C., Kumfert, G. dan Pothen, A. (2001). The computational complexity of the minimum degree algorithm, Proceedings of NIK
2001—14th Norwegian Computer Science Conference, Tromso, Norway, 98–
109.
Hendrickson, B. dan Pothen, A. (2007). Combinatorial scientific computing: The
enabling power of discrete algorithms in computational science, High Performance Computing for Computational Science—VECPAR 2006, M. Dayde,
M. L. M. Palma, L. G. A. Coutinho, E. Pacitti, and J. C. Lopes, eds., Volume 4395 of Lecture Notes in Computer Science, 260–280.
Lipton, R. J., Rose, D. J. dan Tarjan, R. E. (1979). Generalized nested dissection.
SIAM Journal on Numerical Analysis,Volume 16, 346–358
Lipton, R. J. dan Tarjan, R. E. (1979). A separator theorem for planar graphs.
SIAM Journal on Applied Mathematics, Volume 36, 177–189.
Liu, J. W. H. dan Sherman, A. H. (1976). Comparative analysis of the CuthillMcKee and the Reverse Cuthill-McKee ordering algorithms for sparse matrices. SIAM Journal on Numerical Analysis, Volume 13, 198–213.
Universitas Sumatera Utara
43
Liu, J. W. H. (1986). On the storage requirement in the out-of-core multifrontal
method for sparse factor- ization. ACM Transactions on Mathematical Software, Volume 12 , 249–264.
Liu, J. W. H. (1989). The minimum degree ordering with constraints. SIAM Journal on Scientific and Statistical Computing, Volume 10, 1136–1145.
Liu, J. W. H. (1992).The multifrontal method for sparse matrix solution: Theory
and practice. SIAM Review, Volume 34, 82–109.
Olschowka, M. dan Neumaier, A. (1996). A new pivoting strategy for Gaussian
elimination. Linear Algebra and Its Applications, Volume 240, 131–151.
Reid, J. K. dan Scott, J. A. (2006). An out-of-core sparse Cholesky solver, Tech.
Report RAL-TR-2006-013, Computational Sciences and Engineering Department, Rutherford Appleton Laboratory, Oxon, OX11 0QX, England.
Saad, Y. (2003). Iterative Methods for Sparse Linear Systems (Second Edition.SIAM, Amerika.
Tarjan, R. E. (1972). Depth-first search and linear graph algorithms. SIAM Journal
on Computing, Volume 1, 146–160.
Warsito, A. (2009). Fisika Komputasi. FST Universitas Nusa Cendana, NTT.
Yannakakis, M. (1981). Computing the minimum ill-in is NP-complete, SIAM J.
Algebraic Discrete Methods, Volume 2, 77–79.
Universitas Sumatera Utara