Eisenstat, Stanley C.; Liu, Joseph W. H. Algorithmic aspects of elimination trees for sparse unsymmetric matrices. (English) Zbl 1156.65022 SIAM J. Matrix Anal. Appl. 29, No. 4, 1363-1381 (2008). Reviewer: Adhemar Bultheel (Leuven) MSC: 65F05 65F50 05C50 PDFBibTeX XMLCite \textit{S. C. Eisenstat} and \textit{J. W. H. Liu}, SIAM J. Matrix Anal. Appl. 29, No. 4, 1363--1381 (2008; Zbl 1156.65022) Full Text: DOI
Eisenstat, Stanley C.; Liu, Joseph W. H. A tree-based dataflow model for the unsymmetric multifrontal method. (English) Zbl 1120.65316 ETNA, Electron. Trans. Numer. Anal. 21, 1-19 (2005). MSC: 65F05 65F50 65Y05 PDFBibTeX XMLCite \textit{S. C. Eisenstat} and \textit{J. W. H. Liu}, ETNA, Electron. Trans. Numer. Anal. 21, 1--19 (2005; Zbl 1120.65316) Full Text: EuDML
Eisenstat, Stanley C.; Liu, Joseph W. H. The theory of elimination trees for sparse unsymmetric matrices. (English) Zbl 1079.65025 SIAM J. Matrix Anal. Appl. 26, No. 3, 686-705 (2005). Reviewer: R. Militaru (Craiova) MSC: 65F05 65F50 05C50 05C05 PDFBibTeX XMLCite \textit{S. C. Eisenstat} and \textit{J. W. H. Liu}, SIAM J. Matrix Anal. Appl. 26, No. 3, 686--705 (2005; Zbl 1079.65025) Full Text: DOI
Demmel, James W.; Eisenstat, Stanley C.; Gilbert, John R.; Li, Xiaoye S.; Liu, Joseph W. H. A supernodal approach to sparse partial pivoting. (English) Zbl 0931.65022 SIAM J. Matrix Anal. Appl. 20, No. 3, 720-755 (1999). Reviewer: F.Uhlig (Auburn) MSC: 65F05 65F50 15A23 PDFBibTeX XMLCite \textit{J. W. Demmel} et al., SIAM J. Matrix Anal. Appl. 20, No. 3, 720--755 (1999; Zbl 0931.65022) Full Text: DOI
Ashcraft, Cleve; Liu, Joseph W. H. Robust ordering of sparse matrices using multisection. (English) Zbl 0911.65021 SIAM J. Matrix Anal. Appl. 19, No. 3, 816-832 (1998). Reviewer: R.P.Tewarson (Stony Brook) MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{C. Ashcraft} and \textit{J. W. H. Liu}, SIAM J. Matrix Anal. Appl. 19, No. 3, 816--832 (1998; Zbl 0911.65021) Full Text: DOI
Ashcraft, Cleve; Liu, Joseph W. H. Applications of the Dulmage-Mendelsohn decomposition and network flow to graph bisection improvement. (English) Zbl 0907.68138 SIAM J. Matrix Anal. Appl. 19, No. 2, 325-354 (1998). MSC: 68R10 65F05 PDFBibTeX XMLCite \textit{C. Ashcraft} and \textit{J. W. H. Liu}, SIAM J. Matrix Anal. Appl. 19, No. 2, 325--354 (1998; Zbl 0907.68138) Full Text: DOI
Ashcraft, Cleve; Liu, Joseph W. H. Using domain decomposition to find graph bisectors. (English) Zbl 1043.65509 BIT 37, No. 3, 506-534 (1997). MSC: 65F50 65F05 68R10 PDFBibTeX XMLCite \textit{C. Ashcraft} and \textit{J. W. H. Liu}, BIT 37, No. 3, 506--534 (1997; Zbl 1043.65509) Full Text: DOI
Ashcraft, Cleve; Liu, Joseph W. H. Generalized nested dissection: Some recent progress. (English) Zbl 0819.65079 Lewis, John G. (ed.), Applied linear algebra. Proceedings of the 5th SIAM conference, held in Snowbird, UT, USA, June 15-18, 1994. Philadelphia, PA: SIAM. 130-134 (1994). MSC: 65F30 65F05 65F50 PDFBibTeX XMLCite \textit{C. Ashcraft} and \textit{J. W. H. Liu}, in: Applied linear algebra. Proceedings of the 5th SIAM conference, held in Snowbird, UT, USA, June 15-18, 1994. Philadelphia, PA: SIAM. 130--134 (1994; Zbl 0819.65079)
Habashi, W. G.; Robichaud, M.; Nguyen, V.-N.; Ghaly, W. S.; Fortin, M.; Liu, J. W. H. Large-scale computational fluid dynamics by the finite element method. (English) Zbl 0807.76034 Int. J. Numer. Methods Fluids 18, No. 11, 1083-1105 (1994). MSC: 76M10 76N10 65F05 65F10 PDFBibTeX XMLCite \textit{W. G. Habashi} et al., Int. J. Numer. Methods Fluids 18, No. 11, 1083--1105 (1994; Zbl 0807.76034) Full Text: DOI
Eisenstat, Stanley C.; Liu, Joseph W. H. Exploiting structural symmetry in a sparse partial pivoting code. (English) Zbl 0771.65013 SIAM J. Sci. Comput. 14, No. 1, 253-257 (1993). Reviewer: F.Szidarovszky (Tucson) MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{S. C. Eisenstat} and \textit{J. W. H. Liu}, SIAM J. Sci. Comput. 14, No. 1, 253--257 (1993; Zbl 0771.65013) Full Text: DOI Link
Gilbert, John R.; Liu, Joseph W. H. Elimination structures for unsymmetric sparse \(LU\) factors. (English) Zbl 0769.65010 SIAM J. Matrix Anal. Appl. 14, No. 2, 334-352 (1993). Reviewer: L.Berg (Rostock) MSC: 65F05 65F50 05C20 PDFBibTeX XMLCite \textit{J. R. Gilbert} and \textit{J. W. H. Liu}, SIAM J. Matrix Anal. Appl. 14, No. 2, 334--352 (1993; Zbl 0769.65010) Full Text: DOI
Liu, Joseph W. H.; Ng, Esmond G.; Peyton, Barry W. On finding supernodes for sparse matrix computations. (English) Zbl 0765.65034 SIAM J. Matrix Anal. Appl. 14, No. 1, 242-252 (1993). Reviewer: Th.Sonar (Stuttgart) MSC: 65F05 65F50 05C50 PDFBibTeX XMLCite \textit{J. W. H. Liu} et al., SIAM J. Matrix Anal. Appl. 14, No. 1, 242--252 (1993; Zbl 0765.65034) Full Text: DOI Link
Liu, Joseph W. H. The multifrontal method for sparse matrix solution: Theory and practice. (English) Zbl 0919.65019 SIAM Rev. 34, No. 1, 82-109 (1992). MSC: 65F05 65F50 65N30 PDFBibTeX XMLCite \textit{J. W. H. Liu}, SIAM Rev. 34, No. 1, 82--109 (1992; Zbl 0919.65019) Full Text: DOI
Eisenstat, Stanley C.; Liu, Joseph W. H. Exploiting structural symmetry in unsymmetric sparse symbolic factorization. (English) Zbl 0746.65023 SIAM J. Matrix Anal. Appl. 13, No. 1, 202-211 (1992). Reviewer: T.C.Mohan (Madras) MSC: 65F05 65F50 68R10 PDFBibTeX XMLCite \textit{S. C. Eisenstat} and \textit{J. W. H. Liu}, SIAM J. Matrix Anal. Appl. 13, No. 1, 202--211 (1992; Zbl 0746.65023) Full Text: DOI
Liu, Joseph W. H. A generalized envelope method for sparse factorization by rows. (English) Zbl 0900.65064 ACM Trans. Math. Softw. 17, No. 1, 112-129 (1991). MSC: 65F05 65F20 PDFBibTeX XMLCite \textit{J. W. H. Liu}, ACM Trans. Math. Softw. 17, No. 1, 112--129 (1991; Zbl 0900.65064) Full Text: DOI Link
Ashcraft, Cleve; Eisenstat, Stanley C.; Liu, Joseph W. H. A fan-in algorithm for distributed sparse numerical factorization. (English) Zbl 0724.65024 SIAM J. Sci. Stat. Comput. 11, No. 3, 593-599 (1990). Reviewer: O.Widlund (New York) MSC: 65F05 65F50 65Y05 65Y20 PDFBibTeX XMLCite \textit{C. Ashcraft} et al., SIAM J. Sci. Stat. Comput. 11, No. 3, 593--599 (1990; Zbl 0724.65024) Full Text: DOI
Liu, Joseph W. H. The role of elimination trees in sparse factorization. (English) Zbl 0697.65013 SIAM J. Matrix Anal. Appl. 11, No. 1, 134-172 (1990). Reviewer: H.T.Lau MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, SIAM J. Matrix Anal. Appl. 11, No. 1, 134--172 (1990; Zbl 0697.65013) Full Text: DOI
George, Alan; Liu, Joseph W. H.; Ng, Esmond Communication results for parallel sparse Cholesky factorization on a hypercube. (English) Zbl 0687.65024 Parallel Comput. 10, No. 3, 287-298 (1989). Reviewer: M.A.Noor MSC: 65F05 65F50 65Y05 PDFBibTeX XMLCite \textit{A. George} et al., Parallel Comput. 10, No. 3, 287--298 (1989; Zbl 0687.65024) Full Text: DOI
George, Alan; Heath, Michael; Liu, Joseph; Ng, Esmond Solution of sparse positive definite systems on a hypercube. (English) Zbl 0678.65014 J. Comput. Appl. Math. 27, No. 1-2, 129-156 (1989). Reviewer: F.Flandoli MSC: 65F05 65F50 65Y05 PDFBibTeX XMLCite \textit{A. George} et al., J. Comput. Appl. Math. 27, No. 1--2, 129--156 (1989; Zbl 0678.65014) Full Text: DOI
Liu, Joseph W. H. Reordering sparse matrices for parallel elimination. (English) Zbl 0677.65023 Parallel Comput. 11, No. 1, 73-91 (1989). Reviewer: A.Swift MSC: 65F05 65Y05 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, Parallel Comput. 11, No. 1, 73--91 (1989; Zbl 0677.65023) Full Text: DOI
George, Alan; Liu, Joseph W. H. The evolution of the minimum degree ordering algorithm. (English) Zbl 0671.65024 SIAM Rev. 31, No. 1, 1-19 (1989). Reviewer: F.Luban MSC: 65F05 65F50 68Q25 PDFBibTeX XMLCite \textit{A. George} and \textit{J. W. H. Liu}, SIAM Rev. 31, No. 1, 1--19 (1989; Zbl 0671.65024) Full Text: DOI Link
Liu, Joseph W. H. The multifrontal method and paging in sparse Cholesky factorization. (English) Zbl 0900.65062 ACM Trans. Math. Softw. 15, No. 4, 310-325 (1989). MSC: 65F05 65F50 05C50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, ACM Trans. Math. Softw. 15, No. 4, 310--325 (1989; Zbl 0900.65062) Full Text: DOI Link
Liu, Joseph W. H. A graph partitioning by node separators. (English) Zbl 0900.65060 ACM Trans. Math. Softw. 15, No. 3, 198-219 (1989). MSC: 65F05 05C50 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, ACM Trans. Math. Softw. 15, No. 3, 198--219 (1989; Zbl 0900.65060) Full Text: DOI Link
Liu, Joseph W. H. A tree model for sparse symmetric indefinite matrix factorization. (English) Zbl 0653.65021 SIAM J. Matrix Anal. Appl. 9, No. 1, 26-39 (1988). Reviewer: H.Matthies MSC: 65F05 65F50 15A23 PDFBibTeX XMLCite \textit{J. W. H. Liu}, SIAM J. Matrix Anal. Appl. 9, No. 1, 26--39 (1988; Zbl 0653.65021) Full Text: DOI
Liu, Joseph W. H. Equivalent sparse matrix reordering by elimination tree rotations. (English) Zbl 0651.65016 SIAM J. Sci. Stat. Comput. 9, No. 3, 424-444 (1988). Reviewer: S.Filippi MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, SIAM J. Sci. Stat. Comput. 9, No. 3, 424--444 (1988; Zbl 0651.65016) Full Text: DOI
George, Alan; Liu, Joseph; Ng, Esmond A data structure for sparse QR and LU factorizations. (English) Zbl 0648.65019 SIAM J. Sci. Stat. Comput. 9, No. 1, 100-121 (1988). Reviewer: T.F.Coleman MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{A. George} et al., SIAM J. Sci. Stat. Comput. 9, No. 1, 100--121 (1988; Zbl 0648.65019) Full Text: DOI
George, Alan; Heath, Michael T.; Liu, Joseph; Ng, Esmond Sparse Cholesky factorization on a local-memory multiprocessor. (English) Zbl 0642.65018 SIAM J. Sci. Stat. Comput. 9, No. 2, 327-340 (1988). Reviewer: F.Szidarovszky MSC: 65F05 65F50 65Y05 PDFBibTeX XMLCite \textit{A. George} et al., SIAM J. Sci. Stat. Comput. 9, No. 2, 327--340 (1988; Zbl 0642.65018) Full Text: DOI
Liu, Joseph W. H. On threshold pivoting in the multifrontal method for sparse indefinite systems. (English) Zbl 0658.65020 ACM Trans. Math. Softw. 13, 250-261 (1987). Reviewer: S.Filippi MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, ACM Trans. Math. Softw. 13, 250--261 (1987; Zbl 0658.65020) Full Text: DOI Link
Liu, Joseph W. H. A note on sparse factorization in a paging environment. (English) Zbl 0657.65038 SIAM J. Sci. Stat. Comput. 8, 1085-1088 (1987). Reviewer: S.Filippi MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, SIAM J. Sci. Stat. Comput. 8, 1085--1088 (1987; Zbl 0657.65038) Full Text: DOI
Liu, Joseph W. H. An adaptive general sparse out-of-core Cholesky factorization scheme. (English) Zbl 0634.65016 SIAM J. Sci. Stat. Comput. 8, 585-599 (1987). Reviewer: I.Arany MSC: 65F05 65F50 15A23 PDFBibTeX XMLCite \textit{J. W. H. Liu}, SIAM J. Sci. Stat. Comput. 8, 585--599 (1987; Zbl 0634.65016) Full Text: DOI
Liu, Joseph W. H. An application of generalized tree pebbling to sparse matrix factorization. (English) Zbl 0634.65015 SIAM J. Algebraic Discrete Methods 8, 375-395 (1987). Reviewer: I.Arany MSC: 65F05 65F50 05C50 15A23 PDFBibTeX XMLCite \textit{J. W. H. Liu}, SIAM J. Algebraic Discrete Methods 8, 375--395 (1987; Zbl 0634.65015) Full Text: DOI
Liu, Joseph W. H. A partial pivoting strategy for sparse symmetric matrix decomposition. (English) Zbl 0628.65017 ACM Trans. Math. Softw. 13, 173-182 (1987). Reviewer: R.P.Tewarson MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, ACM Trans. Math. Softw. 13, 173--182 (1987; Zbl 0628.65017) Full Text: DOI Link
George, Alan; Liu, Joseph W. H. Householder reflections versus Givens rotations in sparse orthogonal decomposition. (English) Zbl 0619.65018 Linear Algebra Appl. 88-89, 223-238 (1987). Reviewer: A.Varga MSC: 65F05 65F25 65F50 15A23 PDFBibTeX XMLCite \textit{A. George} and \textit{J. W. H. Liu}, Linear Algebra Appl. 88--89, 223--238 (1987; Zbl 0619.65018) Full Text: DOI
George, Alan; Heath, Michael T.; Liu, J. W.-H.; Ng, Esmond Symbolic Cholesky factorization on a local-memory multiprocessor. (English) Zbl 0618.65023 Parallel Comput. 5, 85-95 (1987). Reviewer: J.Šmíd MSC: 65F05 65Y05 65F50 PDFBibTeX XMLCite \textit{A. George} et al., Parallel Comput. 5, 85--95 (1987; Zbl 0618.65023) Full Text: DOI
George, Alan; Liu, Joseph W. H. Compact structural representation of sparse Cholesky, QR and LU factors. (English) Zbl 0677.65022 Computing methods in applied sciences and engineering VII, Proc. 7th Int. Symp., Versailles/France 1985, 93-106 (1986). MSC: 65F05 65F50 PDFBibTeX XML
George, Alan; Heath, Michael T.; Liu, Joseph; Ng, Esmond Solution of sparse positive definite systems on a shared-memory multiprocessor. (English) Zbl 0642.65019 Int. J. Parallel Program. 15, 309-325 (1986). MSC: 65F05 65Y05 65F50 PDFBibTeX XMLCite \textit{A. George} et al., Int. J. Parallel Program. 15, 309--325 (1986; Zbl 0642.65019) Full Text: DOI
Liu, Joseph W. H. On the storage requirement in the out-of-core multifrontal method for sparse factorization. (English) Zbl 0623.65031 ACM Trans. Math. Softw. 12, 249-264 (1986). Reviewer: R.P.Tewarson MSC: 65F05 65F50 15A23 PDFBibTeX XMLCite \textit{J. W. H. Liu}, ACM Trans. Math. Softw. 12, 249--264 (1986; Zbl 0623.65031) Full Text: DOI Link
Liu, Joseph W. H. Computational models and task scheduling for parallel sparse Cholesky factorization. (English) Zbl 0609.65014 Parallel Comput. 3, 327-342 (1986). Reviewer: R.P.Tewarson MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, Parallel Comput. 3, 327--342 (1986; Zbl 0609.65014) Full Text: DOI
Liu, Joseph W. H. A compact row storage scheme for Cholesky factors using elimination trees. (English) Zbl 0605.65015 ACM Trans. Math. Softw. 12, 127-148 (1986). Reviewer: R.P.Tewarson MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, ACM Trans. Math. Softw. 12, 127--148 (1986; Zbl 0605.65015) Full Text: DOI Link
George, Alan; Liu, Joseph; Ng, Esmond Row-ordering schemes for sparse Givens transformations. III. Analyses for a model problem. (English) Zbl 0596.65012 Linear Algebra Appl. 75, 225-240 (1986). Reviewer: A.Bunse-Gerstner MSC: 65F05 65F20 65F50 05C50 PDFBibTeX XMLCite \textit{A. George} et al., Linear Algebra Appl. 75, 225--240 (1986; Zbl 0596.65012) Full Text: DOI
George, Alan; Liu, Joseph; Ng, Esmond Row-ordering schemes for sparse Givens transformations. II. Implicit graph model. (English) Zbl 0596.65011 Linear Algebra Appl. 75, 203-223 (1986). Reviewer: A.Bunse-Gerstner MSC: 65F05 65F50 05C50 PDFBibTeX XMLCite \textit{A. George} et al., Linear Algebra Appl. 75, 203--223 (1986; Zbl 0596.65011) Full Text: DOI
George, Alan; Heath, Michael T.; Liu, Joseph Parallel Cholesky factorization on a shared-memory multiprocessor. (English) Zbl 0587.65017 Linear Algebra Appl. 77, 165-187 (1986). MSC: 65F05 PDFBibTeX XMLCite \textit{A. George} et al., Linear Algebra Appl. 77, 165--187 (1986; Zbl 0587.65017) Full Text: DOI
Liu, Joseph W. H. Modification of the minimum-degree algorithm by multiple elimination. (English) Zbl 0568.65015 ACM Trans. Math. Softw. 11, 141-153 (1985). Reviewer: R.P.Tewarson MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{J. W. H. Liu}, ACM Trans. Math. Softw. 11, 141--153 (1985; Zbl 0568.65015) Full Text: DOI Link
George, Alan; Liu, Joseph; Ng, Esmond Row-ordering schemes for sparse Givens transformations. I. Bipartite graph model. (English) Zbl 0557.65018 Linear Algebra Appl. 61, 55-81 (1984). Reviewer: A.Bunse-Gerstner MSC: 65F05 65F50 PDFBibTeX XMLCite \textit{A. George} et al., Linear Algebra Appl. 61, 55--81 (1984; Zbl 0557.65018) Full Text: DOI
George, Alan; Liu, Joseph W.-H. Computer solution of large sparse positive definite systems. (Chislennoe reshenie bol’shikh razrezhennykh sistem uravnenij). Transl. from the English. (Russian) Zbl 0555.65018 Moskva: Izdatel’stvo ”Mir”. 333 p. R. 1.60 (1984). MSC: 65F05 65-02 15-04 15A23 65F50 PDFBibTeX XML
George, Alan; Liu, Joseph W.-H. Computer solution of large sparse positive definite systems. (English) Zbl 0516.65010 Prentice-Hall Series in Computational Mathematics. Englewood Cliffs, New Jersey: Prentice-Hall, Inc. XII, 324 p. $ 33.70 (1981). MSC: 65F05 15-04 65F50 65-02 15A23 PDFBibTeX XML
George, Alan; Liu, Joseph W. H. A fast implementation of the minimum degree algorithm using quotient graphs. (English) Zbl 0467.65011 ACM Trans. Math. Softw. 6, 337-358 (1980). MSC: 65F05 65F35 68R10 PDFBibTeX XMLCite \textit{A. George} and \textit{J. W. H. Liu}, ACM Trans. Math. Softw. 6, 337--358 (1980; Zbl 0467.65011) Full Text: DOI
George, Alan; Liu, Joseph W. H. A minimal storage implementation of the minimum degree algorithm. (English) Zbl 0424.65006 SIAM J. Numer. Anal. 17, 282-299 (1980). MSC: 65F05 65N30 15A23 PDFBibTeX XMLCite \textit{A. George} and \textit{J. W. H. Liu}, SIAM J. Numer. Anal. 17, 282--299 (1980; Zbl 0424.65006) Full Text: DOI
George, Alan; Liu, Joseph W. H. An automatic nested dissertion algorithm for irregular finite element problems. (English) Zbl 0408.65064 SIAM J. Numer. Anal. 15, 1053-1070 (1978). MSC: 65N30 15A23 65F30 65F05 65N22 PDFBibTeX XMLCite \textit{A. George} and \textit{J. W. H. Liu}, SIAM J. Numer. Anal. 15, 1053--1070 (1978; Zbl 0408.65064) Full Text: DOI
George, Alan; Liu, Joseph W. H. Algorithms for matrix partitioning and the numerical solution of finite element systems. (English) Zbl 0389.65015 SIAM J. Numer. Anal. 15, 297-327 (1978). MSC: 65F05 65N22 65F30 68Q25 PDFBibTeX XMLCite \textit{A. George} and \textit{J. W. H. Liu}, SIAM J. Numer. Anal. 15, 297--327 (1978; Zbl 0389.65015) Full Text: DOI