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- Dexuan Xie
- SIAM J. Scientific Computing
- 2006

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)

- Dexuan Xie, Tamar Schlick
- SIAM Journal on Optimization
- 1999

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)

- Dexuan Xie, Loyce Adams
- SIAM J. Scientific Computing
- 1999

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)

- Dexuan Xie, Tamar Schlick
- 2000

An iterative univariate minimizer (line search) is often used to generate a steplength in each step of a descent method for minimizing a multivariate function. The line search performance strongly depends on the choice of the stopping rule enforced. This termination criterion and other algorithmic details also affect the overall efficiency of the… (More)

- Dexuan Xie
- 1997

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)

- Dexuan Xie
- J. Comput. Physics
- 2014

Article history: Received 11 September 2013 Received in revised form 3 May 2014 Accepted 3 July 2014 Available online 16 July 2014

- Dexuan Xie, Alexander Tropsha, Tamar Schlick
- Journal of Chemical Information and Computer…
- 2000

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)

- Dexuan Xie, Yi Jiang, Peter R. Brune, L. Ridgway Scott
- SIAM J. Scientific Computing
- 2012

- Dexuan Xie, Tamar Schlick
- ACM Trans. Math. Softw.
- 1999

A truncated Newton minimization package, TNPACK, was described in ACM <italic>Transactions on Mathematical Software 14</italic>, 1 (Mar. 1992), pp.46–111. 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)

- Dexuan Xie, Suresh B. Singh, Eugene M. Fluder
- Math. Program.
- 2003

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)