Algorithm construction

Marching Cubes A High Resolution 3D Surface Construction Algorithm, Computer Graphics 21(4), pp 163-169 (1987)... 

The results of both experiments showed that the analysis in the frequency domain provides new technological possibilities of testing characteristics of austenitic steels. Using known phase-frequency characteristics of structural noises it is possible to construct algorithms for separation of useful signal from the defect, even through amplitude values of noise and signal are close in value. 

Rarey M, B Kramer, T Lengauer and G Klebe 1996. A Fast Flexible Docking Method Using a Incremental Construction Algorithm. Journal of Molecular Biology 261 470-489,... 

Unfortunately, fragmentation by construction does not appear to be independent of the random construction algorithm. An alternative method of successive segmentation (Grady and Kipp, 1985) of the surface, as illustrated in Fig. 8.24 leads to a fragment distribution which agrees well with a linear exponential distribution ((8.59)) and differs significantly from the Mott distribution ((8.58)). 

Kramer B, Rarey M, Lengauer T. Evaluation of the FlexX incremental construction algorithm for protein ligand docking. Proteins Struct Fund Genet 1999 37 228-41. 

In an independent investigation on pipeline network calculations using sparse computation techniques, Mah (Ml) devised the following cycle construction algorithm (algorithm MLC) ... 

Rarey, M., Kramer, B., Lengauer, T., and Klebe G. (1996) A fast flexible docking method using an incremental construction algorithm. J. Mol. Biol. 261,470-489. 

Iterative Solution of the Contracted Schrodinger Equation The Reduced Density Matrices Construction Algorithms A. The 2-RDM Construction Algorithm... 

Higher-Order RDMs Construction Algorithms Other Approaches A Unifying Algorithm 1. A Criterion for Selecting the Parameter Value for the 4-RDM... 

A great deal of work has been dedicated by different authors [45, 56, 57, 62, 71-74] to estimate the error matrix A, which was the unknown term in the construction algorithm for the 3-RDM. In fact, the experience of the different authors showed that it was crucial to have a good approximation of this matrix since the error matrix is less determinative in order to achieve convergence in the iterative solution of the CSE. 

Until now the focus has been on the construction algorithms for the 3- and 4-RDMs and the estimation of the A errors. However, the question of how to impose that the RDMs involved as well as the high-order G-matrices be positive must not be overlooked. This condition is not easy to impose in a rigorous way for such large matrices. The renormalization procedure of Valdemoro et al. [54], which was computationally economical but only approximate, acted only on the diagonal elements. 

The indeterminacy of the 2-CSE had caused this equation to be overlooked for many years. In 1992 Valdemoro proposed a method to approximate the 2-RDM in terms of the 1-RDM [108], which was extended in order to approximate the 3- and 4-RDMs in terms of the lower-order matrices [46, 47] and in 1994 Colmenero and Valdemoro [48] applied these approximate constructing algorithms to avoid the indeterminacy problem and solve iteratively the 2-CSE. Since then, the smdy of improved constructing algorithms as well as alternative strategies in the iterative procedure have been proposed [1,6, 15, 18, 36, 49-57, 59, 60, 62-65, 68, 70, 71, 79-85, 109-111]. Also, good results of several calculations have been reported [6, 49-52, 55, 56, 68, 70, 88, 109, 111]. 

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