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The Kronecker Product and Stochastic Automata Networks (2003)  (Make Corrections)  
Amy N. Langville, William J. Stewart



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Abstract: This paper can be thought of as a companion paper to Van Loan's The Ubiquitous Kronecker Product paper [23]. 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. Key words:... (Update)

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BibTeX entry:   (Update)

@misc{ langville-kronecker,
  author = "Amy N. Langville and William J. Stewart",
  title = "The Kronecker Product and Stochastic Automata Networks",
  url = "citeseer.ist.psu.edu/article/langville03kronecker.html" }
Citations (may not include all citations):
326   Topics in Matrix Analysis (context) - Horn, Johnson - 1991
265   Introduction to the Numerical Solution of Markov Chains (context) - Stewart - 1994
140   Kronecker Products and Matrix Calculus with Applications (context) - Graham - 1981
80   the stochastic structure of parallelism and synchronization .. (context) - Plateau - 1985
74   Generalized Inverses of Linear Transformations (context) - Campbell, Meyer - 1979
49   A methodology for solving Markov models of parallel systems (context) - Plateau, Fourneau - 1991
43   PEPS: A package for solving complex Markov models of paralle.. (context) - Plateau - 1990
37   The numerical solution of stochastic automata networks - Stewart, Atif et al. - 1995
29   Stochastic automata network for modelling parallel systems (context) - Plateau, Atif - 1991
21   Matrix Analysis and Applied Linear Algebra (context) - Meyer - 2000
15   The role of the group generalized inverse in the theory of f.. (context) - Meyer - 1975
6   cient descriptor-vector multiplications in stochastic automa.. (context) - Fernandes, Plateau et al. - 1998
6   The Theory of Matrices (context) - MacDu - 1946
5   Projection methods for the analysis of stochastic automata n.. (context) - Buchholz - 1999
5   Kronecker Product of Matrices and Applications (context) - Steeb - 1991
3   Linear and Multilinear Algebra (context) - Henderson, Pukelsheim et al. - 1983
2   The ubiquitous Kronecker product (context) - Van Loan - 2000
2   Approximation with Kronecker products (context) - Pitsianis, Van Loan - 1993
1   A Kronecker product approximate inverse preconditioner for S.. (context) - Langville, Stewart
1   Testing the NKP preconditioner on MCs and SANs (context) - Langville, Stewart
1   the benefits of using functional transitions in Kronecker mo.. (context) - Plateau, Stewart et al. - 2001
1   Stochastic automata networks (context) - Stewart - 2000
1   Preconditioning for Stochastic Automata Networks (context) - Langville - 2002

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