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S.} \newblock {\em Analysis of Sparse Systems}. \newblock PhD thesis, Oxford Univ., England, 1972. \newblock ({Chapters: On a Factored Form of the Inverse for Sparse Matrices, Selecting a Maximal Transversal}). \bibitem[D26]{D26} {Duff, I. S.} \newblock On the number of nonzeros added when {Gaussian} elimination is performed on sparse random matrices. \newblock {\em Math. of Computation}, 28(125):219--230, 1974. \bibitem[D16]{D16} {Duff, I. S.} \newblock On algorithms for obtaining a maximum transversal. \newblock {Tech. Report} CSS-49, Harwell Laboratory, 1976. \bibitem[D11]{D11} {Duff, I. S.} \newblock {MA28}~: {A} set of {FORTRAN} subroutines for sparse unsymmetric linear equations. \newblock {Tech. Report} R-8730, HMSO, AERE Harwell Laboratory, 1977. \bibitem[D7]{D7} {Duff, I. S.} \newblock A survey of sparse matrix research. \newblock {\em Proc. of the IEEE}, 65(4):500--535, 1977. \bibitem[D17]{D17} {Duff, I. S.} \newblock Some current approaches to the solution of large sparse systems of linear equations. \newblock {Tech. Report} CSS-65, Harwell Laboratory, 1978. \bibitem[D69]{D69} {Duff, I. S.} \newblock Practical comparisons of codes for the solution of sparse linear systems. \newblock In {Duff, I. S.} and {Stewart, G. W.}, editors, {\em Sparse Matrix Proceedings 1978}, pages 107--134. SIAM Publications, 1979. \bibitem[D34]{D34} {Duff, I. S.} \newblock Recent developments in the solution of large sparse linear equations. \newblock {Tech. Report} CSS-80, AERE, Harwell Laboratory, 1980. \bibitem[D119]{D119} {Duff, I. S.} \newblock Recent developments in the solution of large sparse linear equations. \newblock In {Glowinski, R.} and {Lions, J. L.}, editors, {\em Computing Methods in Applied Sciences and Engineering}, pages 407--426. North-Holland, 1980. \bibitem[D25]{D25} {Duff, I. S.} \newblock Algorithm 575~: {Permutations} for a zero-free diagonal. \newblock {\em ACM Trans. Math. Software}, 7(3):387--390, 1981. \bibitem[D35]{D35} {Duff, I. S.} \newblock Full matrix techniques in sparse {Gaussian} elimination. \newblock {Tech. Report} CSS-114, AERE, Harwell Laboratory, 1981. \bibitem[D14]{D14} {Duff, I. S.} \newblock {MA32}~: {A} package for solving sparse unsymmetric systems using the frontal method. \newblock {Tech. Report} R-10079, HMSO, AERE Harwell Laboratory, 1981. \bibitem[D42]{D42} {Duff, I. S.} \newblock {ME28}~: {A} sparse unsymmetric linear equation solver for complex equations. \newblock {\em ACM Trans. Math. Software}, 7(4):505--511, 1981. \bibitem[D29]{D29} {Duff, I. S.} \newblock On algorithms for obtaining a maximum transversal. \newblock {\em ACM Trans. Math. Software}, 7(3):315--330, 1981. \bibitem[D45]{D45} {Duff, I. S.} \newblock A sparse future. \newblock In {Duff, I. S.}, editor, {\em Sparse Matrices and Their Uses}, pages 1--29. Academic Press, 1981. \bibitem[D44]{D44} {Duff, I. S.}, editor. \newblock {\em Sparse Matrices and Their Uses}. \newblock Academic Press, 1981. \bibitem[D12]{D12} {Duff, I. S.} \newblock {MA27}~: {A} set of {FORTRAN} subroutines for sparse symmetric linear equations. \newblock {Tech. Report} R-10533, HMSO, AERE Harwell Laboratory, 1982. \bibitem[D33]{D33} {Duff, I. S.} \newblock Research directions in sparse matrix computations. \newblock {Tech. Report} AERE-R-10547, AERE, Harwell Laboratory, 1982. \bibitem[D136]{D136} {Duff, I. S.} \newblock The solution of sparse linear equations on the {CRAY-1}. \newblock {\em CRAY Channels}, 4(3), 1982. \bibitem[D18]{D18} {Duff, I. S.} \newblock A survey of sparse matrix software. \newblock {Tech. Report} R-10512, Computer Science and Systems Division, AERE Harwell Laboratory, Oxfordshire, 1982. \bibitem[D19]{D19} {Duff, I. S.} \newblock Enhancements to the {MA32} package for solving sparse unsymmetric equations. \newblock {Tech. Report} R-11009, HMSO, London, 1983. \bibitem[D10]{D10} {Duff, I. S.} \newblock Data structures, algorithms and software for sparse matrices. \newblock {Tech. Report} 84-1846, Harwell Laboratory, 1984. \bibitem[D39]{D39} {Duff, I. S.} \newblock Design features of a frontal code for solving sparse unsymmetric linear systems out of core. \newblock {\em SIAM J. Sci. and Stat. Comput.}, 5(2):270--280, 1984. \bibitem[D37]{D37} {Duff, I. S.} \newblock Direct methods for solving sparse systems of linear equations. \newblock {\em SIAM J. Sci. and Stat. Comput.}, 5(3):605--619, 1984. \bibitem[D129]{D129} {Duff, I. S.} \newblock The solution of sparse linear equations on the {CRAY-1}. \newblock In {Kowalik, J. S.}, editor, {\em Proceedings of the {NATO} Workshop on High Speed Computation, West Germany}, volume F-7 of {\em {NATO} {ASI} Series}, pages 293--309. Springer-Verlag, 1984. \bibitem[D121]{D121} {Duff, I. S.} \newblock Data structures, algorithms and software for sparse matrices. \newblock In {Evans, D. J.}, editor, {\em Sparsity and its Applications}, pages 1--29. Cambridge University Press, 1985. \bibitem[D9]{D9} {Duff, I. S.}, editor. \newblock {\em Vector and Parallel Processors in Computational Science~: {Proc.} $2^{nd}$ International Conference on Vector and Parallel Processors in Computational Science}. Elsevier Science Publishing Co., 1985. \bibitem[D15]{D15} {Duff, I. S.} \newblock The influence of vector and parallel processors on numerical analysis. \newblock {Tech. Report} AERE-R-12329, Computer Science and Systems Division, Harwell Laboratory, Oxon, England, 1986. \bibitem[D31]{D31} {Duff, I. S.} \newblock Parallel implementation of multifrontal schemes. \newblock {\em Parallel Computing}, 3:193--204, 1986. \bibitem[D130]{D130} {Duff, I. S.} \newblock The parallel solution of sparse linear equations. \newblock In {Handler, W.}, {Haupt, D.}, {Jeltsch, R.}, {Juling, W.}, and {Lange, O.}, editors, {\em {CONPAR} '86}, volume 237 of {\em Lecture Notes in Computer Science}, pages 18--24. Springer-Verlag, 1986. \bibitem[D20]{D20} {Duff, I. S.} \newblock The use of vector and parallel computers in the solution of large sparse linear equations. \newblock {Tech. Report} AERE-R-12393, Computer Science and Systems Division, Harwell Laboratory, Oxon, England, 1986. \bibitem[D22]{D22} {Duff, I. S.} \newblock Multiprocessing a sparse matrix code on the {ALLIANT} {FX/8}. \newblock {Tech. Report} CSS-210, Computer Science and Systems Division, Harwell Laboratory, Oxon, England, 1987. \bibitem[D36]{D36} {Duff, I. S.} \newblock Direct solvers. \newblock {\em Computer Physics Reports}, 11:21--50, 1989. \bibitem[D115]{D115} {Duff, I. S.} \newblock Multiprocessing a sparse matrix code on the {ALLIANT} {FX/8}. \newblock {\em J. Comput. Appl. Math.}, 27:229--239, 1989. \bibitem[D13]{D13} {Duff, I. S.}, {Erisman, A. M.}, {Gear, C. W.}, and {Reid, J. K.} \newblock Some remarks on inverses of sparse matrices. \newblock {Tech. Report} CSS-171, AERE Harwell Laboratory, 1985. \newblock (Also available as Report 51, Mathematics and Computer Science Division, Argonne National Laboratory). \bibitem[D117]{D117} {Duff, I. S.}, {Erisman, A. M.}, and {Reid, J. K.} \newblock A comparison of sparsity orderings for obtaining a pivotal sequence in {Gaussian} elimination. \newblock {\em J. Inst. Math. Appl.}, 14:281--291, 1974. \bibitem[D118]{D118} {Duff, I. S.}, {Erisman, A. M.}, and {Reid, J. K.} \newblock Pivot selection and row ordering in {Givens} reduction on sparse matrices. \newblock {\em Computing}, 13:239--248, 1974. \bibitem[D116]{D116} {Duff, I. S.}, {Erisman, A. M.}, and {Reid, J. K.} \newblock On {George's} nested dissection method. \newblock {\em SIAM J. Numer. Anal.}, 13:686--695, 1976. \bibitem[D6]{D6} {Duff, I. S.}, {Erisman, A. M.}, and {Reid, J. K.} \newblock {\em Direct Methods for Sparse Matrices}. \newblock Clarendon Press, Oxford, 1986. \bibitem[D23]{D23} {Duff, I. S.}, {Gould, N.}, {Lescrenier, M.}, and {Reid, J. K.} \newblock The multifrontal method in a parallel environment. \newblock {Tech. Report} CSS-211, Computer Science and Systems Division, Harwell Laboratory, Oxon, England, 1987. \newblock (Published at {Advances in Numerical Computation, Cox, M. and Hammarling, S., editors, Oxford University Press, 1990}). \bibitem[D24]{D24} {Duff, I. S.}, {Grimes, R. G.}, and {Lewis, J. G.} \newblock Sparse matrix test problems. \newblock {\em ACM Trans. Math. Software}, 15(1):1--14, 1989. \bibitem[D38]{D38} {Duff, I. S.}, {Grimes, R. G.}, and {Lewis, J. G.} \newblock ``{User's Guide}'' for the {Harwell-Boeing} sparse matrix collection ({R}elease {I}). \newblock {Tech. Report} RAL-92-086, Rutherford Appleton Laboratory, 1992. \bibitem[D122]{D122} {Duff, I. S.}, {Grimes, R. G.}, {Lewis, J. G.}, and {Poole, B.} \newblock Sparse matrix test problems. \newblock {\em ACM SIGNUM Newsletter}, 17:22, 1982. \bibitem[D163]{D163} {Duff, I. S.} and {Gustavson, F. G.} \newblock Implementations of the {Hopcroft} and {Karp} maximum matching algorithm. \bibitem[D140]{D140} {Duff, I. S.} and {Johnsson, L.} \newblock The effect of orderings on the parallelization of sparse code. \newblock {Tech. Memorandum}, Mathematics and Computer Science Division, Argonne National Laboratory, 1986. \bibitem[D141]{D141} {Duff, I. S.} and {Johnsson, L.} \newblock Node orderings and concurrency in sparse problems~: {An} experimental investigation. \newblock In {\em Proc. of International Conference on Vector and Parallel Computing, Loen, Norway}, pages 2--6, 1986. \bibitem[D188]{D188} {Duff, I. S.} and {Johnsson, L. S.} \newblock Node orderings and concurrency in structurally-symmetric sparse problems. \newblock In {Carey, G. F.}, editor, {\em Parallel Supercomputing:~ {Methods}, Algorithms, and Applications}, pages 177--189. John Wiley \& Sons, 1989. \bibitem[D131]{D131} {Duff, I. S.} and {Johnsson, S. L.} \newblock Node orderings and concurrency in structurally-symmetric sparse problems. \newblock In {Garey, G. F.}, editor, {\em Parallel Supercomputing~: {Methods}, Algorithms and Applications}, pages 177--189. John Wiley \& Sons, 1988. \bibitem[D32]{D32} {Duff, I. S.}, {Marrone, M.}, and {Radicati, G.} \newblock A proposal for user level sparse {BLAS}. \newblock {Tech. Report} RAL-92-087, Rutherford Appleton Laboratory, 1992. \bibitem[D109]{D109} {Duff, I. S.} and {Meurant, G.} \newblock The effect of ordering on preconditioned conjugate gradients. \newblock {\em BIT}, 29, 1989. \bibitem[D80]{D80} {Duff, I. S.} and {Reid, J. K.} \newblock On the reduction of sparse matrices to condensed forms by similarity transformations. \newblock {\em J. Inst. Math. Appl.}, 15:217--224, 1975. \bibitem[D81]{D81} {Duff, I. S.} and {Reid, J. K.} \newblock A comparison of some methods for the solution of sparse overdetermined systems of linear equations. \newblock {\em J. Inst. Math. Appl.}, 17:267--280, 1976. \bibitem[D28]{D28} {Duff, I. S.} and {Reid, J. K.} \newblock Algorithm 529~: {Permutations} to block tridiagonal form. \newblock {\em ACM Trans. Math. Software}, 4(2):189--192, 1978. \bibitem[D27]{D27} {Duff, I. S.} and {Reid, J. K.} \newblock An implementation of {Tarjan's} algorithm for the block triangulation of a matrix. \newblock {\em ACM Trans. Math. Software}, 4(2):137--147, 1978. \bibitem[D83]{D83} {Duff, I. S.} and {Reid, J. K.} \newblock Performance evaluation of codes for sparse matrix problems. \newblock In {Fosdick, L. D.}, editor, {\em Performance Evaluation of Numerical Software}, pages 121--135. North-Holland, 1979. \bibitem[D41]{D41} {Duff, I. S.} and {Reid, J. K.} \newblock Some design features of a sparse matrix code. \newblock {\em ACM Trans. Math. Software}, 5(1):18--35, 1979. \bibitem[D137]{D137} {Duff, I. S.} and {Reid, J. K.} \newblock Experience of sparse matrix codes on the {CRAY-1}. \newblock {\em Comput. Phys. Comm.}, 76:293--302, 1982. \bibitem[D43]{D43} {Duff, I. S.} and {Reid, J. K.} \newblock The multifrontal solution of indefinite sparse symmetric linear equations. \newblock {\em ACM Trans. Math. Software}, 9(3):302--325, 1983. \bibitem[D40]{D40} {Duff, I. S.} and {Reid, J. K.} \newblock The multifrontal solution of unsymmetric sets of linear equations. \newblock {\em SIAM J. Sci. and Stat. Comput.}, 5(3):633--641, 1984. \bibitem[D176]{D176} {Duff, I. S.} and {Reid, J. K.} \newblock {MA48}:~{A} {FORTRAN} code for direct solution of sparse unsymmetric linear systems of equations. \newblock {Tech. Report} RAL-93-072, Rutherford Appleton Laboratory, Oxon, 1993. \bibitem[D184]{D184} {Duff, I. S.} and {Reid, J. 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