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References
Baker, J.J. "A Note on Multiplying Boolean Matrices", Comm. ACM, 5, 102 (1962)
Barkley, R.W., and Motard, R.L. "Decomposition of Nets", Chem. Eng. J., 3, 265–275 (1972)
Christensen, J.H., and Rudd, D.F. "Structuring Design Computations", AIChE Journal, 15, 94–100 (1969)
Cooper, D.C., and Whitfield, H. "ALP: AN Autocode List-Processing Language", The Computer Journal, 5, 28–32 (1962/3)
Duff, I.S. "A Survey of Sparse Matrix Research", AERE Harwell Report CSS28 (1976)
Duff, I.S., and Reid, J.K. "An Implementation of Tarjan’s Algorithm for the Block Triangularization of a Matrix", AERE Harwell Report CSS29 (1976)
Edmonds, J. "Paths, Trees and Flowers", Can. J. Math., 17, 449–467 (1965)
Edmonds, J., and Johnson, E.L. "Matching: A Well-Solved Class of Integer Linear Programs", in "Combinatorial Structures and Their Applications", pp 88–92, Gordon and Breach, New York (1970)
Garfinkel, R.S., and Nemhauser, G.L. "Integer Programming", J. Wiley and Sons, New York (1972)
Harary, F. "On the Consistency of Precedence Matrices", JACM, 7, 255–259 (1960)
Harary, F. "A Graph Theoretic Approach to Matrix Inversion by Partitioning", Numer. Math. 4, 128–135 (1962a)
Harary, F. "The Determinant of the Adjacency Matrix of a Graph", SIAM Rev., 4, 202–210 (1962b)
Hopcroft, J.E., and Karp, R.M. "An n5/2 Algorithm for Maximum Matchings in Bipartite Graphs", SIAM J. Comput. 2(4), 225–231 (1973)
Jackson, G.D.D. "Interactive Computing in Chemical Plant Design", Ph.D. Thesis, University of London (1976)
Lee, W., and Rudd, D.F. "On the Reordering of Recycle Calculations", AIChE Journal, 12(6), 1184–1190 (1966)
Leigh, M.J. "A Computer Flowsheeting Programme Incorporating Algebraic Analysis of the Problem Structure", Ph.D. Thesis, University of London (1973)
Leigh, M.J., Jackson, G.D.D., and Sargent, R.W.H. "SPEED-UP, a Computer-Based System for the Design of Chemical Processes", CAD 74, Fiche 15 Rows D-E; Int. Conf. and Exhib. on Computers in Engineering and Building Design (1974)
Mah, R.S.H. "A Constructive Algorithm for Computing the Reachability Matrix", AIChE Journal, 20(6), 1227–8 (1974)
Ortega, J.M., and Rheinboldt, W.C. "Iterative Solution of Nonlinear Equations in Several Variables", Academic Press, New York (1970)
Ponstein, J. "Self-Avoiding Paths and the Adjacency Matrix of a Graph", J. SIAM Appl. Math., 14(3), 600–609 (1966)
Sargent, R.W.H., and Westerberg, A.W. "SPEED-UP in Chemical Engineering Design", Trans. Instn. Chem. Engrs., 42, 190–197 (1964)
Steward, D.V. "On an Approach to Techniques for the Analysis of the Structure of Large Systems of Equations", SIAM Rev., 4(4), 321–342 (1962)
Steward, D.V. "Partitioning and Tearing Systems of Equations", J. SIAM Numer. Anal., B2(2), 345–365 (1965)
Strodiot, J.J., and Toint, P.L. "An Algorithm for Finding a Minimum Essential Arc Set of a Directed Graph and its Application in Solving Nonlinear Systems of Equations", Report 76/5, Dept. Mathematique, Facultés Universitaires de Namur (1976)
Tarjan, R. "Depth-First Search and Linear Graph Algorithms", SIAM J. Comput., 1(2), 146–160 (1972)
Upadhye, R.S., and E.A. Grens II. "Selection of Decompositions for Chemical Process Simulation", AIChE Journal, 21(1), 136–143 (1975)
Warshall, S. "A Theorem on Boolean Matrices", JACM 9, 11–12 (1962)
Westerberg, A.W., and Edie, F.C. Computer-Aided Design, Part 1, "Enhancing Convergence Properties by the Choice of Output Variable Assignments in the Solution of Sparse Equation Sets", Chem. Eng. J., 2, 9–16. Part 2, "An Approach to Convergence and Tearing in the Solution of Sparse Equation Sets", ibid., 17–24 (1971)
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Sargent, R.W.H. (1978). The decomposition of systems of procedures and algebraic equations. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067704
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DOI: https://doi.org/10.1007/BFb0067704
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