@article{langville_meyer_2012, title={Who's #1?}, volume={307}, ISSN={["0036-8733"]}, DOI={10.1038/scientificamerican0712-21}, number={1}, journal={SCIENTIFIC AMERICAN}, author={Langville, Amy N. and Meyer, Carl D.}, year={2012}, month={Jul}, pages={21–21} }
@article{langville_meyer_2006, title={A reordering for the PageRank problem}, volume={27}, ISSN={["1095-7197"]}, DOI={10.1137/040607551}, abstractNote={We describe a reordering particularly suited to the PageRank problem, which reduces the computation of the PageRank vector to that of solving a much smaller system and then using forward substitution to get the full solution vector. We compare the theoretical rates of convergence of the original PageRank algorithm to that of the new reordered PageRank algorithm, showing that the new algorithm can do no worse than the original algorithm. We present results of an experimental comparison on five datasets, which demonstrate that the reordered PageRank algorithm can provide a speedup of as much as a factor of 6. We also note potential additional benefits that result from the proposed reordering.}, number={6}, journal={SIAM JOURNAL ON SCIENTIFIC COMPUTING}, author={Langville, AN and Meyer, CD}, year={2006}, pages={2112–2120} }
@article{langville_meyer_2005, title={A survey of eigenvector methods for Web information retrieval}, volume={47}, ISSN={["1095-7200"]}, DOI={10.1137/S0036144503424786}, abstractNote={Web information retrieval is significantly more challenging than traditional well-controlled, small document collection information retrieval. One main difference between traditional information retrieval and Web information retrieval is the Web's hyperlink structure. This structure has been exploited by several of today's leading Web search engines, particularly Google and Teoma. In this survey paper, we focus on Web information retrieval methods that use eigenvector computations, presenting the three popular methods of HITS, PageRank, and SALSA.}, number={1}, journal={SIAM REVIEW}, author={Langville, AN and Meyer, CD}, year={2005}, month={Mar}, pages={135–161} }
@article{langville_stewart_2004, title={Kronecker product approximate preconditioner for SANs}, volume={11}, ISSN={["1099-1506"]}, DOI={10.1002/nla.344}, abstractNote={Many very large Markov chains can be modelled efficiently as stochastic automata networks (SANs). A SAN is composed of individual automata which, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov chain compactly as the sum of Kronecker products of smaller matrices. Thus, storage savings are immediate. The benefit of a SAN's compact representation, known as the descriptor, is often outweighed by its tendency to make analysis of the underlying Markov chain tough. While iterative or projections methods have been used to solve the system πQ=0, the time until these methods converge to the stationary solution π is still unsatisfactory. SAN's compact representation has made the next logical research step of preconditioning thorny. Several preconditioners for SANs have been proposed and tested, yet each has enjoyed little or no success. Encouraged by the recent success of approximate inverses as preconditioners, we have explored their potential as SAN preconditioners. One particularly relevant finding on approximate inverse preconditioning is the nearest Kronecker product approximation discovered by Pitsianis and Van Loan. In this paper, we extend the nearest Kronecker product technique to approximate the Q matrix for an SAN with a Kronecker product, A1 ⊗ A2 ⊗…⊗ AN. Then, we take M = A ⊗ A ⊗…⊗ A as our SAN NKP preconditioner. Copyright © 2004 John Wiley & Sons, Ltd.}, number={8-9}, journal={NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS}, author={Langville, AN and Stewart, WJ}, year={2004}, pages={723–752} }
@article{langville_stewart_2004, title={Special issue devoted to papers presented at the Conference on the Numerical Solution of Markov Chains 2003 - Preface}, volume={386}, ISSN={["1873-1856"]}, DOI={10.1016/j.laa.2004.02.016}, journal={LINEAR ALGEBRA AND ITS APPLICATIONS}, author={Langville, AN and Stewart, WJ}, year={2004}, month={Jul}, pages={1–2} }
@article{langville_stewart_2004, title={Testing the nearest Kronecker product preconditioner on Markov chains and stochastic automata networks}, volume={16}, ISSN={["1526-5528"]}, DOI={10.1287/ijoc.1030.0041}, abstractNote={This paper is the experimental follow-up to Langville and Stewart (2002), where the theoretical background for the nearest Kronecker product (NKP) preconditioner was developed. Here we test the NKP preconditioner on both Markov chains (MCs) and stochastic automata networks (SANs). We conclude that the NKP preconditioner is not appropriate for general MCs, but is very effective for a MC stored as a SAN.}, number={3}, journal={INFORMS JOURNAL ON COMPUTING}, author={Langville, AN and Stewart, WJ}, year={2004}, pages={300–315} }
@article{langville_stewart_2004, title={The Kronecker product and stochastic automata networks}, volume={167}, ISSN={["1879-1778"]}, DOI={10.1016/j.cam.2003.10.010}, abstractNote={This paper can be thought of as a companion paper to Van Loan's The Ubiquitous Kronecker Product paper (J. Comput. Appl. Math. 123 (2000) 85). We collect and catalog the most useful properties of the Kronecker product and present them in one place. We prove several new properties that we discovered in our search for a stochastic automata network preconditioner. We conclude by describing one application of the Kronecker product, omitted from Van Loan's list of applications, namely stochastic automata networks.}, number={2}, journal={JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS}, author={Langville, AN and Stewart, WJ}, year={2004}, month={Jun}, pages={429–447} }
@article{basharin_langville_naumov_2004, title={The life and work of A.A. Markov}, volume={386}, number={Jul 15 2004}, journal={Linear Algebra and Its Applications}, author={Basharin, G. P. and Langville, A. N. and Naumov, V. A.}, year={2004}, pages={26-} }