*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,*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).*Uncoupling the Perron eigenvector problem,*Linear Algebra and Its Appl., Vol. 114/115, 1989, pp. 69--94.*Stochastic complementation, uncoupling Markov chains, and the theory of nearly reducible systems,*(pdf), SIAM Rev., Vol 31, No. 2, 1989, pp. 240--272.*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,*Linear Algebra and Its Appl., Vol., 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,*Linear Algebra and Its Applications, 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). -
*Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization,*(pdf), NCSU Technical Report Math 81706, to be submitted, (co-author with Russell Albright, James Cox, David Duling, and Amy Langville). -
*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*to appear in the*Journal of Quantitative Analysis in Sports*(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,*SIAM J. on Matrix Analysis and Applications, Vol. 33, No.4, pp. 1214-1236, 2012. (co-author with Charles Wessell). -
*Determining the Number of Clusters via Iterative Consensus Clustering,*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,*Pattern Recognition, September, 2013, submitted, (co-author with Shaina Race). -
*Continuity of the Perron Root*, May, 2014. To appear in Linear and Multilinear Algebra.

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