Publications In Chronological Order

• Note on the computation of the generalized inverse of a matrix, SIAM Rev., 8(1966), pp. 522-524, (co-author with F. A. Graybill and R. J. Painter).
• On ranks of pseudoinverses, SIAM Rev., 11(1969), pp. 382-385.
• On the construction of solutions to the matrix equations AX = A and YA = A, SIAM Rev., (1969), pp. 612-615.
• Note on a least squares inverse for a matrix, J. of the Assoc. for Comp Machinery, 17(1970), pp. 110-112, (co-author with R. J. Painter).
• Generalized inverses of triangular matrices, SIAM J. Appl. Math., 18(1970), pp. 401-406.
• On the rank of the sum of two rectangular matrices, Canadian Math. Bull., 12(1969), pg. 508.
• Some remarks on EPr matrices and generalized inverses, Linear Algebra and Its Appl., 3(1970), pp.741-750.
• Generalized inverses of block triangular matrices, SIAM J. Appl. Math., 19(1970), pp. 741-750.
• Representations for (1)- and (1,2)-inverses for partitioned matrices, Linear Algebra and Its Appl., 4(1971), pp. 221-232.
• The Moore-Penrose inverse of a bordered matrix, Linear Algebra and Its Appl., 5(1972), pp. 375-382.
• Generalized inversion of modified matrices, SIAM J. Appl. Math., 24(1973), pp. 315-323.
• Generalized inverses and ranks of block matrices, SIAM J. Appl. Math., 25(1973), pp.597-602.
• Limits and the index of a square matrix, SIAM J. Appl. Math., 26(1974), pp. 469-478.
• Generalized inverses of the fundamental bordered matrix used in linear estimation, SANKHYA, Series A, 37(1975), pp. 428-438, (Co-author with F. J. Hall).
• EPr operators and generalized inverses, The Canadian Math. Bull., 3(1975), pp. 327-333, (Co-author with S. L. Campbell).
• Continuity properties of the Drazin inverse, Linear Algebra and Its Appl., 10(1975), pp. 77-83, (Co-author with S. L. Campbell).
• The role of the group generalized inverse in the theory of finite Markov chains, SIAM Rev., 17(1974), pp. 443-464.
• Applications of the Drazin inverse to linear systems of differential equations, SIAM J. Appl. Math., 31(1974), pp. 411-425, (Co-author with S. L. Campbell and N. J. Rose).
• The index and the Drazin inverse of block triangular matrices, SIAM J. Appl. Math., 33(1977), pp. 1-7, (Co-author with N. J. Rose).
• Weak Drazin inverses, Linear Algebra and Its Appl., 20(1978), pp. 167-178, (Co-author with S. L. Campbell).
• Convergent powers of a matrix with applications to iterative methods for singular linear systems, SIAM J. Num. Anal., 14(1977), pp. 699-705, (Co-author with R. J. Plemmons).
• An alternative expression for the mean first passage matrix, Linear Algebra and Its Appl., 22(1978), pp. 41-47.
• Singular M-matrices and inverse positivity, Linear Algebra and Its Appl., 22(1978), pp. 129-156, (Co-author with M. W. Stadelmaier).
• Updating methods for finite Markov chains, J. Stat. Comp. and Simulation, 11(1980), pp. 163-181, (Co-author with J. M. Shoaf).
• Analysis of finite Markov chains by group inversion techniques, Recent Applications of Generalized Inverses, Pitman Research Notes Series, Pitman Pub. Co., 1982.
• The condition of a Markov chain and perturbation bounds for the limiting probabilities, SIAM J. Algebraic and Discrete Methods, 1(1980), pp. 273-283.
• Nonnegative matrices with power invariant zero patterns, Linear Algebra and Its Applications, 29(1982), pp. 23-29, (Co-author with G. Poole, N. J. Rose, and M. W. Stadelmaier).
• History of Gaussian Elimination, (pdf), The 1982 Mathematical Calendar, Rome Press.
• Generalized inverses of linear transformations, Pitman Publishing Co., Ltd., London, 1979, (Co-author with S. L. Campbell).
• Creative Computer Programming, Hayden Publishing Co., Inc., Rochell Park, NJ, 1980, (Co-author with H. Sagan).
• Using the QR factorization and group inversion to compute, differentiate, and estimate the sensitivity of stationary probabilities for Markov chains, SIAM J. on Algebraic and Discrete Methods, 17(1986), pp. 273-281, (Co-author with G. H. Golub).
• Sensitivity of the stationary distribution vector for an ergodic Markov chain, Linear Algebra and Its Appl., 17(1986), pp. 1-16, (Co-author with R. E. Funderlic).
• Derivatives and perturbations of eigenvectors, (pdf), SIAM J. Num. Anal., 25(1988), pp. 679-691 (Co-author with G. W. Stewart).
• Orthogonal reduction on vector computers, SIAM J. Sci. Stat. Comp., Vol 10, No. 2, 1989, pp. 372--381. (Co-author with J. M. Ortega and R. B. Mattingly).
• Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems, (pdf), SIAM Rev., Vol 31, No. 2, 1989, pp. 240--272.
***Download the original journal copy here (pdf)***
• Uncoupling the Perron eigenvector problem (pdf), Linear Algebra and Its Appl., Vol. 114/115, 1989, pp. 69--94.
• Stochastic Complementation and the GTH algorithm for Markov Chains, NCSU Center For Research in Scientific Computation Tech. Report #11228801 (Co-author with R. B. Mattingly).
• Computing the stationary distribution vector of an irreducible Markov chain on a shared-memory multiprocessor, Numerical Solution Of Markov Chains, Probability: Pure and Applied, Vol 8, pp. 491--508, Ed. by W. J. Stewart, Marcel Dekker, New York, (Co-author with R. B. Mattingly).
• A general framework for aggregation disaggregation methods for the numerical solution of Markov chains, Proceedings of the NSF Design and Manufacturing System Conference, 1992, (Co-author with H. D. Kafeety and W. J. Stewart).
• The Character of a Markov Chain, Linear Algebra, Markov Chains, and Queuing Models, IMA Volumes in Mathematics and its Applications, Vol. 48, 1993, Springer-Verlag, pp~47--58.
• Sensitivity of Markov chains, IMA Series #919, Feb., 1992.
• Aggregation/disaggregation methods for the numerical solution of Markov chains, a general framework, NCSU Tech. Report, (Co-author with H. D. Kafeety and W. J. Stewart).
• Sensitivity of Markov chains, SIAM J. Matrix Anal. Appl., Vol 15, 1994, pp. 715--728.
• Uniform stability of Markov chains, SIAM J. Matrix Anal. Appl., Vol 15, 1994, pp. 1061--1074 (co-author with I. Ipsen).
• Linear Algebra, Markov Chains, and Queuing Models, IMA Volume 48, 1993, Edited by C. D. Meyer and R. J. Plemmons, Springer Verlag, New York.
• An explicit preconditioner for the conjugate gradient method, SIAM Proc. Cornelius Lanczos International Centenary Conference, 1994, pp. 294--296, (Co-author with M. Benzi).
• The character of a finite Markov Chain, Invited IMA contribution to Linear Algebra, Markov Chains, and Queueing Models, IMA Volumes in Mathematics and its Applications, Vol. 48, Springer-Verlag, 1994.
• Error analysis of aggregation/disaggregation, NCSU Math. Tech. Report #NA-019401, to be submitted, 1995.
• A direct project projection method for sparse linear systems, SIAM J. Sci. Comput. Vol. 16, No. 5, September, 1995, pp. 1159-1176 (co-author with M. Benzi).
• The angle between complementary subspaces, The American Mathematical Monthly, 102(1995), pp. 904--911, (co-author with Ilse Ipsen).
• Steps towards an iterative rank-revealing method, Boeing Information and Support Services Tech. Report ISSTECH-95-013, November 30, 1995 (co-author with D Pierce).
• A sparse approximate inverse preconditioner for the conjugate gradient method, SIAM J. Sci. Comput. Vol. 17, No. 3, September, 1996, pp. 1135-1149. , (co-author with M. Benzi and M. Tuma).
• Convergence estimates for solution of integral equations with GMRES, J. Integral Equations and Appl., 8(1996), (co-author with S. L. Campbell, I. C. F. Ipsen, and C. T. Kelley and Z. Q. Xue).
• GMRES and the minimum polynomial, BIT, 36(1996), pp. 32--43, (co-author with S. Campbell, I. Ipsen, C. Kelley).
• On the structure of stochastic matrices with a subdominant eigenvalue near 1, (pdf), Linear Algebra and Its Appl.,272(1998), pp.193--203, (co-author with D. J. Hartfiel).
• The idea behind Krylov methods, American Mathematical Monthly, Vol. 105, No. 10, December, 1998, pp. 889--899, (with I. Ipsen).
• Markov Chain Sensitivity Measured By Mean First Passage Times, Linear Algebra and Its Applications, 316(2000), pp. 21-28, (co-author with Grace E. Cho).
• Matrix Analysis and Applied Linear Algebra, SIAM (Text Book) , 2000, ISBN 0-89871-454-0.
• Comparison of perturbation bounds for the stationary distribution of a Markov chain, (pdf), Linear Algebra and Its Applications, 335(2001), pp. 137-150, (co-author with Grace E. Cho).
• Comparison of perturbation bounds for the stationary distribution of a Markov chain, Linear Algebra and Its Applications, September, 335(2001), pp. 137-150, (co-author with Grace E. Cho).
• Eudoxus meets Cayley, American Mathematical Monthly, Volume 110, Number 10, December 2003, pp. 912-927, (co-author with Richard Chandler and Nick Rose).
• Preconditioning KKT systems, Numer. Linear Algebra Appl., 2001. (co-author with John Haws).
• Preconditioning KKT systems, The Boeing Co., M&CT-Tech-01-021, 2003, (co-author with John Haws).
• Fiddling with PageRank, (pdf), CRSC Tech. Report CRSC-TR03-34, September, 2003, (co-author with Amy N. Langville).
• A survey of eigenvector methods of web information retrieval, (pdf), SIAM Review, Vol 47, No. 1, March 2005, pp. 135-161 (co-author with Amy N. Langville).
• Deeper inside PageRank, (pdf), Internet Mathmathematics, Vol. 1, No. 3, 2005, pp.335-400. (co-author with Amy N. Langville).
• Updating PageRank with Iterative Aggregation, (pdf), Proc. WWW2004, May 17-22, 2004, New York, NY, ACM 1-58113-912 8/04/0005 pp.392-394. (co-author with Amy N. Langville).
• The Use of Linear Algebra by Web Search Engines, (pdf), Bulletin of the International Linear Algebra Society, No. 33, Dec. 2005, pp. 2-6. (co-author with Amy N. Langville).
• Updating Markov chains with an eye on Google's PageRank, (pdf), SIAM J. Matrix Analysis and Applications, Vol 27, No. 4, pp. 968-987, 2006. (co-author with Amy N. Langville).
• A Reordering For The PageRank Problem, (pdf), SIAM J. Sci. Stat. Comp., (SISC), Vol. 27, No.6, 2006, pp. 2112-2120. (co-author with Amy N. Langville).
• Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, ISBN: 0-691-12202-4, 2006, (co-author with Amy N. Langville).
• Information Retrieval and Web Search, (pdf), Chapter 63, The Handbook of Linear Algebra, Chapman & Hall/CRC, ISBN: 1584885106, 2006, Leslie Hogben (editor). (co-author with Amy N. Langville).
• Initializations for the Nonnegative Matrix Factorization, (pdf), Proc. of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, (co-author with Amy N. Langville and R. Albright).
• Updating Markov Chains, (pdf), Proc. of the A. A. Markov Aniversary Converence, Charleston, SC, pp. 229-238, June 12-14, 2006, (co-author with A. Langville).
• An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix, (pdf), PhD dissertation, North Carolina State University, Applied Mathematics, March 3, 2007, Prakash Chanchana (directed by C. D. Meyer). Also available here.

• Generalizing Google's PageRank to Rank National Football League Teams, (pdf), Proceedings of SAS Global Forum 2008, San Antonio, TX, March 16-19, 2008, Article 151-2008, (co-author with Russell Albright and Anjela Govan).
• Offense-Defense Approach to Ranking Team Sports, (pdf), Vol 5, No. 1, 2009, Article 4, Journal of Quantitative Analysis in Sports, (co-author with Anjela Govan).
• Beating the Spread: Predicting Game Outcomes with a New Ranking Model, Proceedings of the SAS M2008 Data Mining Conference, Las Vegas, NV, October 26-29, 2008. (co-author with Anjela Govan, Amy Langville, Russell Albright).
• Rush vs Pass: Modeling the NFL (co-author with Ralph Abbey, John Holodnak, Chandler May, and Dan Moeller,).
• Spectral Clustering and Visualization: A Novel Clustering of Fisher's Iris Data Set, SIAM SIURO, Vol 4, pp. 1-15, 2011. (co-author with D. Benson-Putnins, M. Bonfardin, M. Magnoni, D. Martin, and C. Wessell).
• Why No Ranking System Is No. 1, Scientific American, July, 2012.
• An Approach to Identify the Number of Clusters, SIAM Undergraduate Research Online (SIURO), Volume 5, December 18, 2012, (co-author with Katelyn Gao, Heather Hardeman, Edward Lim, Cristian Potter, Ralph Abbey).
• Stochastic Data Clustering (pdf), SIAM J. on Matrix Analysis and Applications, Vol. 33, No.4, pp. 1214-1236, 2012. (co-author with Charles Wessell). Wessell PhD Thesis.pdf (Directed by C. D. Meyer)
• Determining the Number of Clusters via Iterative Consensus Clustering, ArXiv: 1408.0967, Proceedings of SDM2013, 2013 International Conference on Data Mining, Austin, Texas, May, 2013, (co-author with Shaina Race and Kevin Valakuzhy).
• A Flexible Framework for Consensus Clustering, ArXiv: 1408.0972, Pattern Recognition, 2014, (co-author with Shaina Race).
• Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization,, ArXiv: 1407.7299, SAS Technical Report, 2014 (co-author with Russell Albright, James Cox, David Duling, and Amy Langville).
• Continuity of the Perron Root, ArXiv: 1407.7564, Linear and Multilinear Algebra, July 3, 2014, http://dx.doi.org/10.1080/03081087.2014.934233.
• A Case Study in Text Mining: Interpreting Twitter Data from World Cup Tweets, ArXiv: 1408.5427, Submitted, SIAM Review, August, 2014, (co-author with Carol Sadek, Daniel Godfrey, Cayley Johns, Shaina Race).
• Relations Between Adjacency and Modularity Graph Partitioning, ArXiv: 1505.03481, Submitted, SIMAX, May, 2015, (co-author with Hansi Jiang).
• Rank My Update Please, The American Mathematical Monthly, 125:1, pp. 61-64, 2018 https://doi.org/10.1080/00029890.2017.1389199.