By a News Reporter-Staff News Editor at Computer Weekly News -- Investigators publish new report on Scientific Computing. According to news reporting originating in Kent, Ohio, by VerticalNews journalists, research stated, "Large-scale networks arise in many applications. It is often of interest to be able to identify the most important nodes of a network or to ascertain the ease of traveling between nodes."
The news reporters obtained a quote from the research from Kent State University, "These and related quantities can be determined by evaluating expressions of the form u(T) f(A) w, where A is the adjacency matrix that represents the graph of the network, f is a nonlinear function, such as the exponential function, and u and w are vectors, for instance, axis vectors. This paper describes a novel technique for determining upper and lower bounds for expressions u(T) f(A) w when A is symmetric and bounds for many vectors u and w are desired. The bounds are computed by first evaluating a low-rank approximation of A, which is used to determine rough bounds for the desired quantities for all nodes. These rough bounds indicate for which vectors u and w more accurate bounds should be computed with the aid of Gauss-type quadrature rules. This hybrid approach is cheaper than only using Gauss-type rules to determine accurate upper and lower bounds in the common situation when it is not known a priori for which vectors u and w accurate bounds for u(T) f(A) w should be computed."
According to the news reporters, the research concluded: "Several computed examples, including an application to software engineering, illustrate the performance of the hybrid method."
For more information on this research see: Network Analysis Via Partial Spectral Factorization And Gauss Quadrature. SIAM Journal on Scientific Computing, 2013;35(4):A2046-A2068. SIAM Journal on Scientific Computing can be contacted at: Siam Publications, 3600 Univ City Science Center, Philadelphia, PA 19104-2688, USA.
Our news correspondents report that additional information may be obtained by contacting C. Fenu, Kent State University, Dept. of Math Sci, Kent, OH 44242, United States. Additional authors for this research include D. Martin, L. Reichel and G. Rodriguez.
Keywords for this news article include: Kent, Ohio, United States, Scientific Computing, North and Central America
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