Suely Oliveira

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In this paper we present new algorithms for spectral graph partitioning. Previously, the best partitioning methods were based on a combination of Combinatorial algorithms and application of the Lanczos method when the graph allows this method to be cheap enough. Our new algorithms are purely spectral. They calculate the Fiedler vector of the original graph(More)
The generalized Davidson algorithm can be seen as a method which uses preconditioned residuals to create a subspace where it is easier to nd the smallest eigenvalue and its eigenvector. In this paper theoretical results proving convergence rates are shown. In addition, we investigate the use of multigrid as a preconditioner for this method and describe a(More)
Identifying functional modules is believed to reveal most cellular processes. There have been many computational approaches to investigate the underlying biological structures [9, 4, 10, 6]. A spectral clustering method plays a critical role identifying functional modules in a yeast protein-protein network in [6, 4]. We present an unweighted-graph version(More)
Accurately computing the singular values of long products of matrices is important for estimating Lyapunov exponents: λ i = limn→∞(1/n) log σ i (An · · · A 1). Algorithms for computing singular values of products in fact compute the singular values of a perturbed product (An + En) · · · (A 1 + E 1). The question is how small are the relative errors of the(More)
Rutishauser, Gragg and Harrod and finally H.Y. Zha used the same class of chasing algorithms for transforming arrowhead matrices to tridi-agonal form. Using a graphical theoretical approach, we propose a new chasing algorithm. Although this algorithm has the same sequential computational complexity and backward error properties as the old algorithms, it is(More)
The problem of partitioning a graph such that the number of edges incident to vertices in diierent partitions is minimized, arises in many contexts. Some examples include its recursive application for minimizing ll-in in matrix factorizations and load-balancing for parallel algorithms. Spectral graph partitioning algorithms partition a graph using the(More)
Identifying functional modules is believed to reveal most cellular processes. There have been many computational approaches to investigate the underlying biological structures (Bader and Hogue, 2003; Dhillon et al., 2005; Krogan et al., 2006; Ramadan et al., 2005; Xiong et al., 2005; Zhang et al., 2004). A spectral clustering method plays a critical role(More)