Fast algorithms

Greengard L and Rokhlin V 1987 A fast algorithm for particle simulations J. Comput. Phys. 73 325—48... 

Lin, M., Hsieh, J., Du, D. H. C., Thomas, J. P., MacDonald, J. A. Distributed network computing over local ATM networks. In Proceedings of Supercomputing 94. IEEE Computer Society Press, Los Alamitos, California, 1994. Greengard, L., Rokhlin, V. A fast algorithm for particle simulation. J. Comp. Phys. 73 (1987) 325-348. 

Greengard L 1994. Fast Algorithms for Classical Physics. Science 265 909-914. 

Greengard L and V 1 Roklin 1987. A Fast Algorithm for Particle Simulations. Journal of Computational Physics 73 325-348. 

Holiday J D, S R Ranade and P Willett 1995. A Fast Algorithm For Selecting Sets Of Dissimilar Molecule From Large Chemical Databases. Quantitative Structure-Activity Relationships 14 501-506. 

In an SCFcalculation, many iterations may be needed to achieve SCFconvergence. In each iteration all the two-electron integrals are retrieved to form a Fock matrix. Fast algorithms to retrieve the two-electrons integrals are important. 

Powell, M. J. D. A Fast Algorithm for Nonlinearly Constrained Optimization Calculations, Lecture Notes in Mathematics 630 (1977). 

Bush, I. E., Fast Algorithms for Digital Smoothing Filters, Anal. Chem. 55, 1983, 2353-2361. 

When applied to QSAR studies, the activity of molecule u is calculated simply as the average activity of the K nearest neighbors of molecule u. An optimal K value is selected by the optimization through the classification of a test set of samples or by the leave-one-out cross-validation. Many variations of the kNN method have been proposed in the past, and new and fast algorithms have continued to appear in recent years. The automated variable selection kNN QSAR technique optimizes the selection of descriptors to obtain the best models [20]. 

Representation of each molecular orbital as a linear combination of atomic orbitals (atomic basis sets). Atomic basis sets are usually represented as Slater type orbitals or as combinations of Gaussian functions. The latter is very popular, due to a very fast algorithm for the computation of bielectronic integrals. 

End-Bridging Monte Carlo A Fast Algorithm for Atomistic Simulation of Condensed Phases of Long Polymer Chains. 

There are a multitude of methods for this task. Those that are conceptually simple usually are computationally intensive and slow, while the fast algorithms have a more complex mathematical background. We start this chapter with the Newton-Gauss-Levenberg/Marquardt algorithm, not because it is the simplest but because it is the most powerful and fastest method. We can t think of many instances where it is advantageous to use an alternative algorithm. 

Holliday, J.D., Ranade, S.S., and Willett, P. A fast algorithm for selecting sets of dissimilar molecules from large chemical databases. Quant. Struc.-Act. Relat. 1995, 14, 501-506. 

Even though restoration in two distinct spectral bands leads to very fast algorithms, it is still not optimum because of the residual error in the low-frequency band of spectral components used as a region of support. Perhaps the requirement that the inverse-filtered low-frequency spectrum (or, equivalently, its corresponding spatial function) be held constant for the restoration... 

Bersohn, M. A., A Fast Algorithm for Calculation of the Distance Matrix of a Molecule. 

Computational Methods. Since finding the intersection of G(x) and p A - x requires an expensive iterative algorithm with variable convergence times, it is not well suited for real-time operation. In this section, fast algorithms based on precomputed nonlinearities are described. 

Malvar, 1991] Malvar, H. S. (1991). Extended lapped transforms Fast algorithms and applications. In Proc. IEEE Int. Conf. Acoust., Speech and Signal Proc, pages 1797- 1800. 

The important problem of how to decide whether a given benzenoid system possesses Kekule structures or not has been investigated for a long time. The first fast algorithm was given by Sachs [5]. Recently necessary and sufficient structural requirements for the existence of Kekule structures in benzenoid systems have been discovered [6, 7], but these results do not provide a rapid method for recognizing Kekulean benzenoid systems. Also the P-V maximum flow method of He and He [8,9] should be mentioned. More recently the present author [10] put forward an algorithm which is much simpler and faster than that of Sachs. 

Zhang, K., Shasha, D. Simple fast algorithms for the editing distance between trees and related problems. SIAM Journal of Computing 1989, 18, 1245-1262. 

The docking calculations are usually iterated separately for each molecule of a database. Since the calculation times per molecule are still quite large even for fast algorithms (about a minute per ligand), the use of a workstation cluster or parallel hardware is of great advantage. Within FlexX, a task... 

Rousseeuw, P.J. and Van Driessen, K., A fast algorithm for the minimum covariance determinant estimator, Technometrics, 41, 212-223, 1999. 

Croux, C. and Ruiz-Gazen, A., A fast algorithm for robust principal components based on projection pursuit, in COMPSTAT1996 (Barcelona), Physica, Heidelberg, 1996, pp. 211-217. 

Iterative resolution methods are in general more versatile than noniterative methods. They can be applied to more diverse problems, e.g., data sets with partial or incomplete selectivity in the concentration or spectral domains, and to data sets with concentration profiles that evolve sequentially or nonsequentially. Prior knowledge about the data set (chemical or related to mathematical features) can be used in the optimization process, but it is not strictly necessary. The main complaint about iterative resolution methods has often been the longer calculation times required to obtain optimal results however, improved fast algorithms and more powerful PCs have overcome this historical limitation. 

SIGMOD International Conference on Management of Data, Philadelphia, PA, 1999, pp. 61-72. Fast Algorithms for Projected Clustering. 

T. HoUebeek, T.S. Ho, H. Rabitz, A fast algorithm for evaluating multidimensional potential energy surfaces, /. Chem. Phys. 106 (17) (1997) 7223-7227. 

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