Matrix Market Bibliography

This is a bibliography of works related to matrices distributed by the Matrix Market. It includes all the references in the User Guides to the Harwell Boeing Collection (Release I) and the NEP Collection.

• E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorenson. LAPACK Users' Guide, 2nd Edition. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1995.

• M. Arioli, I.S. Duff, N.I.M. Gould, and J.K. Reid. Use of the p⁴ and p⁵ algorithms for in-core factorization of sparse matrices. SIAM Journal of Scientific Computing, 11:913-927, 1990.

• Mario Arioli, Iain Duff, and Daniel Ruiz. Stopping criteria for iterative solvers. SIAM Journal of Matrix Analysis and Applications, 13:138-144, 1992.

• Mario Arioli, Iain S. Duff, Daniel Ruiz, and Miloud Sadkane. Block Lanczos techniques for accelerating the block Cimmino method. SIAM Journal of Scientific Computing, 16:1478-1511, 1995.

• B. A. Armstrong. Near minimal matrix profiles and wavefronts for testing nodal resequencing algorithms. International Journal of Numerical Methods Engineering, 21:1785-1790, 1986.

• Cleve Ashcraft and Roger Grimes. The influence of relaxed supernode partitions on the multifrontal method. ACM Transactions on Mathematical Software, 15(4):291-309, December 1989.

• Cleve Ashcraft. Compressed graphs and the minimum degree algorithm. SIAM Journal of Scientific Computing, 16:1404-1411, 1995.

• Z. Bai and G. W. Stewart. SRRIT - a FORTRAN subroutine to calculate the dominant invariant subspaces of a nonsymmetric matrix. Comp. Sci. Dept. Tech. Rep. TR-2908, University of Maryland, College Park, Maryland, April 1992.

• Zhaojun Bai, David Day, James Demmel, and Jack Dongarra. A test matrix collection for non-Hermitian eigenvalue problems, release 1.0, September 1996. (PostScript)

• Michele Benzi and Carl D. Meyer. A direct projection method for sparse linear systems. SIAM Journal of Scientific Computing, 16:1157-1176, 1995.

• Michele Benzi and Miroslav Tuma. A sparse approximate inverse prteconditioner for nonsymmetric linear systems. SIAM Journal of Scientific Computing, 19:968-994, 1998.

• Michele Benzi, Carl D. Meyer, and Miroslav Tuma. A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM Journal of Scientific Computing, 17:1135-1149, 1996.

• M. Benzi, R. Kouhia, and M. Tuma. An assessment of some preconditioning techniques in shell problems. Technical Report LA-UR-97-3892, Los Alamos National Laboratory, Los Alamos, NM, September 1997. (PostScript)

• Ronald F. Boisvert and Bruce R. Miller. Enhancing the interactivity of software and data repositories with Java. In A. Sydow, editor, Artificial Intelligence and Computer Science, volume 4 of Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, pages 767-772, Berlin, 1997. Wissenshaft & Technik Verlag. (PostScript)

• Ronald F. Boisvert, Roldan Pozo, and Karin Remington. The Matrix Market exchange formats: Initial design. Technical Report NISTIR 5935, National Institute of Standards and Technology, Gaithersburg, MD, USA, December 1996. (PostScript)

• Ronald F. Boisvert, Roldan Pozo, Karin Remington, Richard Barrett, and Jack J. Dongarra. The Matrix Market: A web resource for test matrix collections. In Ronald F. Boisvert, editor, Quality of Numerical Software, Assessment and Enhancement, pages 125-137, London, 1997. Chapman & Hall. (PostScript)

• Ronald F. Boisvert, editor. Quality of Numerical Software, Assessment and Enhancement. Chapman & Hall, London, 1997.

• J. G. L. Booten, P. M. Meijer, H. J. J. te Riele, and H. A. van der Vorst. Parallel Arnoldi method for the construction of a krylov subspace basis an application in magnetohydrodynamics. In W. Gentzsch and U. Harms, editors, Vol. II: Networking and Tools, volume 797 of Lecture Note in Computer Science, Berlin, 1994. Springer-Verlag. (Proceedings of the International Conference and Exhibition on High-Performance Computing and Networking, Munich, Germany, April 1994).

• F. Cachard. Logiciel numerique associé à une modélisation de systèmes informatiques. Master's thesis, Université Scientifique et Médicale de Grenoble et l'Institut National Polytechnique de Grenoble, 1981.

• M. Carlsson. Unknown. Technical Report 33, Uppsala Observatory, 1985.

• Ian A. Cavers. A hybrid tridiagonalization algorithm for symmetric sparse matrices. SIAM Journal of Matrix Analysis and Applications, 15:1363-1380, 1994.

• Françoise Chaitin-Chatelin. Is nonnormality a serious computational difficulty in practice. In Ronald F. Boisvert, editor, Quality of Numerical Software, Assessment and Enhancement, pages 300-314, London, 1997. Chapman & Hall.

• Françoise Chatelin and S. Godet-Thobie. Stability analysis in aeronautical industries. In M. Durand and F. El Dabaghi, editors, Proceedings of the 2nd Symposium on High-Performance Computing, Montpellier, France, pages 415-422. Elsevier North-Holland, 1991.

• M.-D. Choi. Tricks or treats with the Hilbert matrix. American Mathematical Monthly, 90:301-312, 1983.

• Edmond Chow and Yousef Saad. Experimental study of ILU preconditioners for indefinite matrices. Journal of Computational and Applied Mathematics, 86:387-414, 1997.

• Edmond Chow and Yousef Saad. Approximate inverse preconditioners via sparse-sparse iterations. SIAM Journal of Scientific Computing, 19:995-1023, 1998.

• S. I. Chu. Complex quasivibrational energy formalism for intense-field multiphoton and above-threshold dissociation: complex scaling fourier-grid Hamiltonian method. Journal of Computational Physics, 94(2):7901-7909, 1991.

• B. A. Cipra. An introduction to the Ising model. American Mathematical Monthly, 94:937-959, 1987.

• P.A. Clement. A class of triple-diagonal matrices for test purposes. SIAM Review, 1:50-52, 1959.

• A.K. Cline and R.K. Rew. A set of counter-examples to three condition number estimators. SIAM Journal of Scientific and Statistical Computing, 4:602-611, 1983.

• A. K. Cline, G. H. Golub, and G. W. Platzman. Calculations of normal modes of oceans using a Lanczos method. In J. R. Bunch and D. J. Rose, editors, Sparse Matrix Computations, pages 409-426. Academic Press, London and New York, 1976.

• John M. Conroy, Steven G. Kratzer, Robert F. Lucas, and Aaron E. Naiman. Data-parallel sparse LU factorization. SIAM Journal of Scientific Computing, 19:584-604, 1998.

• M. Creutz. Quarks, Gluons, and Lattices. Cambridge University Press, 1986.

• J. Cullum and R. A. Willoughby. A practical procedure for computing eigenvalues of large sparse nonsymmetric matrices. In J. Cullum and R. A. Willoughby, editors, Large Scale Eigenvalue Problems, Amsterdam, 1986. Elsevier Science Pub., North-Holland.

• J. Cullum, W. Kerner, and R. Willoughby. A generalized nonsymmetric Lanczos procedure. Computer Physics Communications, 53:19-48, 1989.

• Timothy A. Davis and Iain S. Duff. An unsymmetric pattern multifrontal method for sparse LU factorization. SIAM Journal of Matrix Analysis and Applications, 18:140-158, 1997.

• Michel J. Dayde, Jean-Yves L'Excellent, and Nicholas I.M. Gould. Element-by-element preconditioners for large partially seperable optimization problems. SIAM Journal of Scientific Computing, 18:1767-1787, 1997.

• P. B. Dixon, B. R. Parmenter, J. Sutton, and D. P. Vincent. ORANI: A Multisectoral Model of the Australian Economy. North Holland, Amsterdam, 1982.

• H. Dong, A. Chronopoulos, J. Zou, and A. Gopinath. Vectorial integrated difference analysis of dielectric waveguides, 1993.

• F. W. Dorr. An example of ill-conditioning in the numerical solution of singular perturbation problems. Mathematics of Computation, 25:271-283, 1971.

• I. S. Duff and J. K. Reid. A comparison of sparsity orderings for obtaining a pivotal sequence in Gaussian elimination. Journal of the Institute for Mathematics and Applications, 14:281-291, 1974.

• I.S. Duff and J. K. Reid. Performance evaluation of codes for sparse matrix problems. In L. D. Fosdick, editor, Performance Evaluation of Numerical Software, pages 121-135. North Holland, Amsterdam, New York and London, 1979.

• I.S. Duff and J.K. Reid. The design of MA48: A code for the direct solution of sparse unsymmetric linear systems of equations. ACM Transactions on Mathematical Software, 22:187-226, 1996.

• I.S. Duff and J.K. Reid. Exploiting zeros on the diagonal in the direct solution of indefinite sparse symmetric linear systems. ACM Transactions on Mathematical Software, 22:227-257, 1996.

• I. S. Duff and J. A. Scott. Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration. ACM Transactions on Mathematical Software, 19:137-159, 1993.

• Iain S. Duff and J. A. Scott. The design of a new frontal code for solving sparse, unsymmetric systems. ACM Transactions on Mathematical Software, 22(1):30-45, March 1996.

• I. S. Duff, A. M. Erisman, and J. K. Reid. Direct Methods for Sparse Matrices. Oxford University Press, 1986.

• I. S. Duff, R. G. Grimes, and J. G. Lewis. Sparse matrix test problems. ACM Transactions on Mathematical Software, 15(1):1-14, March 1989.

• I.S. Duff, N.I.M. Gould, J.K. Reid, and K. Turner. The factorization of sparse symmetric indefinite matrices. IMA Journal of Numerical Analysis, 11:181-204, 1991.

• Iain Duff, Roger G. Grimes, and John G. Lewis. Users' guide for the Harwell-Boeing sparse matrix collection (Release I). Technical Report TR/PA/92/86, CERFACS, October 1992. (PostScript)

• P. J. Eberlein. A note on the matrices denoted by b_n. SIAM Journal of Applied Mathematics, 20:87-92, 1971.

• A. Edelman and E. Kostlan. The road from Kac's matrix to Kac's random polynomials. In John G. Lewis, editor, Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, pages 503-507. SIAM, Philadelphia, 1994.

• Stanley C. Eisenstat and Joseph W.H. Liu. Exploiting structural symmetry in unsymmetric sparse symbolic factorization. SIAM Journal of Matrix Analysis and Applications, 13:202-211, 1992.

• Stanley C. Eisenstat and Joseph W. H. Liu. Exploiting structural symmetry in a sparse partial pivoting code. SIAM Journal of Scientific Computing, 14:253-257, 1993.

• H. C. Elman and R. L Streit. Polynomial iteration for nonsymmetric indefinite linear systems. In J. P. Hennart, editor, Numerical Analysis Proceedings, Gauuajsato, Mexico, volume 1230 of Lecture Notes in Mathematics, Berlin, 1984. Springer-Verlag.

• I. Emiris. Sparse Elimination and Applications in Kinematics. PhD thesis, Computer Science Division, University of California at Berkeley, 1993.

• A. M. Erisman, R. G. Grimes, J. G. Lewis, and W. G. Poole Jr. A structurally stable modification of Hellerman- Rarick's P^4 algorithm for reordering unsymmetric sparse matrices. SIAM Journal of Numerical Analysis, 22:369-385, 1985.

• A. M. Erisman, R. G. Grimes, J. G. Lewis, W. G. Poole Jr., and H. D. Simon. Evaluation of orderings for unsymmetric sparse matrices. SIAM Journal of Scientific and Statistical Computing, 8:600-624, 1987.

• G. C. Everstine. A comparison of three resequencing algorithms for the reduction of matrix profile and wavefront. International Journal of Numerical Methods Engineering, 14:837-853, 1979.

• W. Feller. An introduction to probability theory and its applications. John Wiley, New York, 1961.

• F. A. Fernandez and Y. Lu. Variational finite element analysis of dielectric waveguides with non spurious solutions. Electron. Letter., 26(25):2125-2126, 1990.

• Fluid Dynamics International, Inc., Evanston, Illinois. FIDAP 7.0 Examples Manual, 1993.

• W. L. Frank. Computing eigenvalues of complex matrices by by determinant evaluation and by methods of Danilewski and Wielandt. Journal of the Society for Industrial and Applied Mathematics, 6:378-392, 1958.

• Roland W. Freund and Noel M. Nachtigal. An inplementation of the QMR method based on coupled two-term recurrences. SIAM Journal of Scientific Computing, 15:313-337, 1994.

• B. Friedman. Eigenvalues of composite matrices. Proc. Cambridge Philos. Soc., 57:37-49, 1961.

• A. Galick, T. Kerhoven, and U. Ravaioli. Iterative solution of the eigenvalue problem for a dielectric waveguide. IEEE Trans. Micro. Theory Tech., 40:699-705, 1992.

• T. J. Garratt. The numerical detection of Hopf bifurcations in large systems arising in fluid mechanics. PhD thesis, University of Bath, UK, 1991.

• C. W. Gear. A simple set of test matrices for eigenvalue programs. Mathematics of Computation, 23:119-125, 1969.

• S. Gedney and U.D. Navsariwala, 1996. personal communication.

• A. George and J. W. H. Liu. Computer Solution of Large Sparse Positive-Definite Systems. Prentice-Hall, Englewood Cliffs, NJ, 1981.

• John R. Gilbert, Esmong G. Ng, and Barry W. Peyton. An efficient algorithm to compute row and column counts for sparse cholesky factorization. SIAM Journal of Matrix Analysis and Applications, 15:1075-1091, 1994.

• S. Godet-Thobie. Eigenvalues of large highly nonnormal matrices. PhD thesis, Paris IX Dauphine University, France, 1992. Also CERFACS thesis report TH/PA/93/06.

• G.H. Golub and J.H. Wilkinson. Ill-conditioned eigensystems and the computation of the jordan canonical form. SIAM Review, 18:578-619, 1976.

• Nicholas I.M. Gould and Jennifer A. Scott. Sparse approximate-inverse preconditioners using norm-minimization techniques. SIAM Journal of Scientific Computing, 19:605-625, 1998.

• J. Grcar. Operator coefficient methods for linear equations. Report SAND89-8691, Sandia National Laboratory, November 1989.

• R. G. Grimes, J. G. Lewis, and H. D. Simon. Experiences in solving large eigenvalue problems on the CRAY X-MP. Technical Report ETA-TR-40, ETA Division of Boeing Computer Services, Seattle, WA, 1986.

• Roger G. Grimes, John G. Lewis, and Horst D. Simon. A shifted block Lanczos algorithm for solving sparse symmetric eigenproblems. SIAM Journal of Matrix Analysis and Applications, 15:228-272, 1994.

• B. D. Hassard, N. Kazarinoff, and Y. H. Wan. Theory and Applications of Hopf Bifurcation. Cambridge University Press, Cambridge, 1981.

• R. F. Heinemann and A. B. Poore. Multiplicity, stability, and oscillatory dynamics of a tubular reactor. Chem. Eng. Sci., 36:1411-1419, 1981.

• Nicholas J. Higham and Desmond J. Higham. Gaussian elimination with pivoting. SIAM Journal of Matrix Analysis and Applications, 10:155-164, 1989.

• Nicholas J. Higham. A survey of condition number estimation for triangular matrices. SIAM Review, 29:575-596, 1987.

• Nicholas J. Higham. Algorithm 694: A collection of test matrices in MATLAB. ACM Transactions on Mathematical Software, 17(3):289-305, September 1991.

• Nicholas J. Higham. The Test Matrix Toolbox for Matlab (version 3.0). Numerical Analysis Report No. 276, Manchester Centre for Computational Mathematics, Manchester, England, September 1995. (PostScript)

• Nicholas J. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia, 1996.

• P. J. Holmes, editor. Waves in distributed chemical systems: experiments and computations, Philadelphia, 1980. SIAM. Proceedings of the Asilomar Conference Ground, Pacific Grove, California, 1979.

• P. S. Jensen and W. A. Loden. Supplementary study on the sensitivity of optimized structures. Technical Report LMSC-D777859, Lockheed Palo Alto Research Laboratory, 1980.

• Z. Jia. Some numerical methods for large unsymmetric eigenproblems. PhD thesis, The faculty of Mathematics, University of Bielefeld, Germany, February 1994.

• J. Jin. The finite element method in electromagnetics. John Wiley & Sons, New York, 1993.

• W. Kahan. Numerical linear algebra. Canadian Mathematical Bulletin, 9:757-801, 1966.

• B. Kaufman. Crystal statistics ii. Phys. Rev., 76:1232, 1949.

• W. Kerner. Large-scale complex eigenvalue problems. Journal of Computational Physics, 85(1):1-85, 1989.

• D. E. Knuth. The Art of Computer Programming, Volume 1, Fundamental Algorithms. Addison-Wesley, Reading, Massachussetts, second edition, 1973.

• M. N. Kooper, H. A. van der Vorst, S. Poedts, and J.P. Goedbloed. Application of the implicitly updated arnoldi methods with a complex shift and invert strategy in mhd. Journal of Computational Physics, 118:320-328, 1995.

• P. Lauchli. Jordan-elimination und ausgleichung nach kleinsten quadraten. Numerische Mathematik, 3:226-240, 1961.

• R. B. Lehoucq. Analysis and Implementation of an Implicitly Restarted Arnoldi Iteration. PhD thesis, Department of Computational and Applied Mathematics, Rice University, Houston, Texas, May 1995. (Also appeared as Technical Report TR95-13).

• J. G. Lewis and R. G. Grimes. Practical Lanczos algorithms for solving structural engineering eigenvalue problems. In I. S. Duff, editor, Sparse Matrices and Their Uses, pages 349-355. Academic Press, New York and London, 1981.

• J. G. Lewis and W. G. Poole. Ordering algorithms applied to sparse matrices in electrical power problems. In Neves Erisman and Dwarakanath, editors, Unknown, pages 115-124. Unknown, 1980.

• J. G. Lewis and H. D. Simon. Numerical experience with the spectral transformation Lanczos method. Technical Report MM-TR-16, ETA Division of Boeing Computer Services, Seattle, WA, 1984.

• J. G. Lewis and H. D. Simon. The impact of hardware Gather/Scatter on sparse Gaussian elimination. Technical Report ETA TR-33, ETA Division of Boeing Computer Services, Seattle, WA, 1986.

• John G. Lewis, Barry W. Peyton, and Alex Pothen. A fast algorithm for reordering sparse matrices for parallel factorization. SIAM Journal of Scientific Computing, 10:1146-1173, 1989.

• J. G. Lewis. Algorithms for sparse matrix eigenvalue problems. Technical Report CS-77-595, Stanford University, Stanford, CA, 1977.

• J. G. Lewis. Implementation of the Gibbs-Poole-Stockmeyer and Gibbs-King algorithms. ACM Transactions on Mathematical Software, 8(2):180-189 and 190-194, 1982.

• J. G. Lewis. Numerical experiments with SPARSPAK. SIGNUM Newsletter, 18(3):12-22, 1983. Association for Computing Machinery.

• J. W. H. Liu. An adaptive out-of-core Cholesky factorization scheme. Technical Report CS-85-05, Department of Computer Science at York University, Ontario, Canada, 1985.

• J. W. H. Liu. Modification of the minimum degree algorithm by multiple elimination. ACM Transactions on Mathematical Software, 11(2):141-153, 1985.

• J. W. H. Liu. On the storage requirement in the out-of-core multifrontal method for sparse factorization. Technical Report CS-85-02, Department of Computer Science at York University, Ontario, Canada, 1985.

• Joseph W. H. Liu. A compact row storage scheme for Cholesky factors using elimination trees. ACM Transactions on Mathematical Software, 12(2):127-148, June 1986.

• Joseph W. H. Liu. On threshold pivoting in the multifrontal method for sparse indefinite systems. ACM Transactions on Mathematical Software, 13(3):250-261, September 1987.

• Joseph W. H. Liu. A partial pivoting strategy for sparse symmetric matrix. ACM Transactions on Mathematical Software, 13(2):173-182, June 1987.

• Joseph W. H. Liu. A graph partitioning algorithm by node separators. ACM Transactions on Mathematical Software, 15(3):198-219, September 1989.

• Joseph W. H. Liu. The multifrontal method and paging in sparse Cholesky factorization. ACM Transactions on Mathematical Software, 15(4):310-325, December 1989.

• Joseph W.H. Liu. The minimum degree ordering with constraints. SIAM Journal of Scientific Computing, 10:1136-1145, 1989.

• Joseph W. H. Liu. A generalized envelope method for sparse factorization by rows. ACM Transactions on Mathematical Software, 17(1):112-129, March 1991.

• M. Lotkin. A set of test matrices. Mathematical Tables and Other Aids to Computation, 9:153-161, 1955.

• Szu-Min Lu and Jesse L. Barlow. Multifrontal computation with the orthogonal factors of sparse matrices. SIAM Journal of Matrix Analysis and Applications, 17:658-679, 1996.

• A. Mahajan, E. H. Dowell, and D. Bliss. Eigenvalue calculation procedure for an Euler-Navier-Stokes solver with applications to flows over airfoils. Journal of Computational Physics, 97:398-413, 1991.

• D. Manocha and J. Canny. Multipolynomial resultant algorithms. Computer science division report, University of California, Berkeley, 1993.

• T. A. Manteuffel. An incomplete factorization technique for positive definite linear systems. Mathematics of Computation, 34:473-497, 1980.

• M. Marcus and H. Minc. A Survey of Matrix Theory and Matrix Inequalities. Dover, New York, 1992.

• L. Marro. Méthodes de Réduction de la largeur de bande et du profil efficace des matrices creuses. PhD thesis, Université de Nice, 1980.

• L. Marro. A linear time implementation of profile reduction algorithms for sparse matrices. SIAM Journal of Scientific and Statistical Computing, 7:1212-1231, 1986.

• K. Meerbergen and D. Roose. Matrix transformation for computing rightmost eigenvalues of large sparse nonsymmetric matrices. Report TW 209, Department of Computer Science, Katholieke Universiteit Leuven, Belgium, 1994. (Revised April 1995).

• K. Meerbergen and A. Spence. A spectral transformation for finding complex eigenvalues of large sparse nonsymmetric matrices. Report TW 219, Department of Computer Science, Katholieke Universiteit Leuven, Belgium, 1994.

• I. Montvay and G. Munster. Quantum Fields on the Lattice. Cambridge University Press, 1994.

• L. Reichel N. M. Nachtigal and L. N. Trefethen. A hybrid GMRES algorithm for nonsymmetric linear systems. SIAM Journal of Matrix Analysis and Applications, 13:796-825, 1992.

• J. C. Nash. Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation. Adam Hilger, Bristol, second edition, 1990.

• M. Newman and J. Todd. The evaluation of matrix inversion programs. Journal of the Society for Industrial and Applied Mathematics, 6:466-476, 1958.

• Esmond Ng and Barry W. Payton. A supernodal cholesky factorization algorithm for shared-memory multiprocessors. SIAM Journal of Scientific Computing, 14:761-769, 1993.

• Esmond G. Ng and Barry W. Peyton. Block sparse Cholesky algorithm on uniprocessor computers. SIAM Journal of Scientific Computing, 14:1034-1056, 1993.

• Bureau of Economic Analysis. Definitions and conventions of the 1972 Input-Output study, July 1980. Staff Paper BEA-SP-80-034.

• W. E. Olmstead, W. E. Davis, S. H. Rosenblat, and W. L. Kath. Bifurcation with memory. SIAM Journal of Applied Mathematics, 46:171-188, 1986.

• B. Parlett and W. Heng. The method of minimal representations in 2d Ising model calculations. Journal of Computational Physics, 114:257-264, 1994.

• K. R. Pearson and R. J. Rimmer. An efficient method for the solution of large computable general equilibrium models. In Sixth Biennial Conference of the Simulation Society of Australia, August 1984.

• K. R. Pearson and R. J. Rimmer. Sparse matrix methods on the VAX 11/780. In Proceedings of the 24th European DECUS Symposium, Amsterdam, September 1984.

• G. W. Platzman. Normal modes of the Atlantic and Indian Oceans. Journal of Physical Oceanography, 5:201-221, 1975.

• Alex Pothen and Fernando L. Alvarado. A fast reordering algorithm for parallel sparse triangular solution. SIAM Journal of Scientific Computing, 13:645-653, 1992.

• Alex Pothen and Chin-Ju Fan. Computing the block triangular form of a sparse matrix. ACM Transactions on Mathematical Software, 16(4):303-324, December 1990.

• Alex Pothen and Chunguang Sun. A mapping algorithm for parallel sparse Cholesky factorization. SIAM Journal of Scientific Computing, 14:1253-1257, 1993.

• Alex Pothen, Horst D. Simon, and Kang-Pu Liou. Partioning sparse matrices with eigenvectors of graphs. SIAM Journal of Matrix Analysis and Applications, 11:430-452, 1990.

• Klaus J. Ressel and Martin H. Gutknecht. QMR smoothing for Lanczos-type product methods based on three-term recurrences. SIAM Journal of Scientific Computing, 19:55-73, 1998.

• Thomas H. Robey and Deborah L. Sulsky. Row ordering for a sparse QR decomposition. SIAM Journal of Matrix Analysis and Applications, 15:1208-1225, 1994.

• Edward Rothberg and Anoop Gupta. Efficient sparse matrix factorization on high performance workstations -- exploiting the memory hierarchy. ACM Transactions on Mathematical Software, 17(3):313-334, September 1991.

• Edward Rothberg and Anoop Gupta. An effecient block-orientated approach to parallel sparse Cholesky factorization. SIAM Journal of Scientific Computing, 15:1413-1439, 1994.

• Edward Rothberg. Performance of panel and block approaches to sparse Cholesky factorization on the iPSC/860 and paragon multicomputers. SIAM Journal of Scientific Computing, 17:699-713, 1996.

• A. Ruhe. Rational Krylov, a practical algorithm for large sparse nonsymmetric matrix pencils. Computer Science Division Report UCB/CSD-95-871, University of California, Berkeley, April 1995.

• H. Rutishauser. On test matrices. In Programmation en Mathematiques Numeriques, pages 349-365. Editions Centre Nat. Recherche Sci., Paris, 165, 1966.

• Y. Saad. Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices. Linear Algebra and Applications, 34:269-295, 1980.

• Youcef Saad. Krylov subspace methods on supercomputers. SIAM Journal of Scientific Computing, 10:1200-1232, 1989.

• Y. Saad. Numerical Methods for Large Eigenvalue Problems. Halsted Press, Div. of John Wiley & Sons, Inc., New York, 1992.

• Yosef Saad. SPARSKIT: A basic tool kit for sparse matrix computations. Technical report, Computer Science Department, University of Minnesota, Minneapolis, MN 55455, June 1994. Version 2. (PostScript)

• Yosef Saad. Preconditioned Krylov subspace methods for CFD applications. In W. G. Hasbashi, editor, Solution Techniques for Large Scale CFD Problems, page 141. (publisher unknown), 1995.

• Y. Saad. ILUM: A multi-elimination ILU preconditioner for general sparse matrices. SIAM Journal of Scientific Computing, 17:830-847, 1996.

• P. E. Saylor. Richardson's iteration with dynamic parameters and the SIP incomplete factorization for the solution of linear systems of equations. Society of Petroleum Engineers Journal, pages 691-708, 1981.

• G. B. Scharmer and M. Carlsson. A new approach to multi-level non-LTE radiative transfer problems. Journal of Computational Physics, 38, 1985.

• B. Schultz. Bounded waveguide eigenmodes, finite element method solution. Master's thesis, Department of Electrical Engineering, University of Kentucky, 1994.

• H. D. Simon. The Lanczos algorithm with partial reorthogonalization. Mathematics of Computation, 42:115-142, 1984.

• H. D. Simon. Incomplete LU preconditioned conjugate-gradient-like methods in reservoir simulation. In Proceeding of the 8th SPE Symposium on Reservoir Simulation, Dallas, TX, February 1985.

• A. M. Siriwaranda. A Multisectoral General Equilibrium Model of Tariff Protection in the Colony of Victoria in 1880. PhD thesis, La Trobe University, Australia, 1985.

• P. B. Slater. Migration regions of the United States: Two County-Level 1965-70 analyses. Technical report, Community and Organization Research Institute University of California-Santa Barbara, Santa Barbara, CA, 1983.

• Gerald L.G. Sleijpen and Henk A. van der Vorst. A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM Journal of Matrix Analysis and Applications, 17:401-425, 1996.

• W. F. Smyth and J. Dunn. Results of tests on matrix bandwidth and profile reduction algorithms. Technical report, Department of Computer Science and Systems at McMaster University, Ontario, Canada, 1986.

• Andreas Stathopolous, Youcef Saad, and Kesheng Wu. Dynamic thick restarting of the Davidson, and the implicitly restarted Arnoldi methods. SIAM Journal of Scientific Computing, 19:227-245, 1998.

• W. J. Stewart and A. Jennings. A simultaneous iteration algorithm for real matrices. ACM Transactions on Mathematical Software, 7:184-198, 1981.

• G. W. Stewart. SRRIT - a FORTRAN subroutine to calculate the dominant invariant subspaces of a nonsymmetric matrix. Comp. Sci. Dept. Tech. Rep. TR-514, University of Maryland, College Park, Maryland, November 1978.

• W. J. Stewart. A comparison of numerical techniques in markov modeling. Communications of the ACM, 21(2):144-152, 1978.

• D. B. Szyld. Using sparse matrix techniques to solve a model of the world economy. In I. S. Duff, editor, Sparse Matrices and Their Uses, pages 357-365. Academic Press, New York and London, 1981.

• J. Tan and G. Pan. A new edge element analysis of dispersive waveguiding structures. IEEE Trans. Micro. Theory Tech., 43(11):2600-2607, 1995.

• O. Taussky and J. Todd. Another look at a matrix of Mark Kac. Linear Algebra and Applications, 150:341-360, 1991.

• A. Frank van der Stappen, Rob H. Bisseling, and Johannes G.G. van de Vorst. Parallel sparse LU decomposition on a mesh network of transputers. SIAM Journal of Matrix Analysis and Applications, 14:853-879, 1993.

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