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As the development of the PSOR method (a point parallel SOR method by mesh domain partitioning proposed in [SIAM J. Sci. Comput., 20 (1999), pp. 2261–2281], this paper introduces a new mesh domain partition and ordering (the multitype partition and ordering), and proposes a new block parallel SOR (BPSOR) method for numerically solving 2-dimensional (2D) or(More)
To e ciently implement the truncated-Newton (TN) optimization method for largescale, highly nonlinear functions in chemistry, an unconventional modi ed Cholesky (UMC) factorization is proposed to avoid large modi cations to a problem-derived preconditioner, used in the inner loop in approximating the TN search vector at each step. The main motivation is to(More)
In this paper we propose and analyze a new parallel SOR method, the PSOR method, formulated by using domain partitioning and interprocessor data communication techniques. We prove that the PSOR method has the same asymptotic rate of convergence as the Red/Black (R/B) SOR method for the five-point stencil on both strip and block partitions, and as the(More)
A simple way to avoid idle processors in implementing the multigrid method on a parallel computer is to select a proper ner grid as the new coarsest grid. For clarity, the variant of the V-cycle generated by this approach is called the U-cycle in this paper. It is proved that the U-cycle with a ner coarsest grid can have a faster convergence rate, and the(More)
A rapid algorithm for visualizing large chemical databases in a low-dimensional space (2D or 3D) is presented as a first step in database analysis and design applications. The projection mapping of the compound database (described as vectors in the high-dimensional space of chemical descriptors) is based on the singular value decomposition (SVD) combined(More)
A truncated Newton minimization package, TNPACK, was described in ACM <italic>Transactions on Mathematical Software 14</italic>, 1 (Mar. 1992), pp.46&#8211;111. Modifications to enhance performance, especially for large-scale minimization of molecular potential functions, are described here. They involve three program segments of TNPACK: negative curvature(More)
The similarity and diversity sampling problems are two challenging optimization tasks that arise in the analysis of chemical databases. As a first step to their solution, we propose an efficient projection/ refinement protocol based on the principal component analysis (PCA) and the truncated-Newton minimization method implemented by our package TNPACK(More)