%0 Journal Article %1 Liu2009RotationMatrixOptimization %A Liu, Pu %A Agrafiotis, Dimitris K. %A Theobald, Douglas L. %D 2010 %I Wiley Subscription Services, Inc., A Wiley Company %J Journal of Computational Chemistry %K %N 7 %P 1561--1563 %R 10.1002/jcc.21439 %T Fast determination of the optimal rotational matrix for macromolecular superpositions %U http://dx.doi.org/10.1002/jcc.21439 %V 31 %X Finding the rotational matrix that minimizes the sum of squared deviations between two vectors is an important problem in bioinformatics and crystallography. Traditional algorithms involve the inversion or decomposition of a 3 × 3 or 4 × 4 matrix, which can be computationally expensive and numerically unstable in certain cases. Here, we present a simple and robust algorithm to rapidly determine the optimal rotation using a Newton-Raphson quaternion-based method and an adjoint matrix. Our method is at least an order of magnitude more efficient than conventional inversion/decomposition methods, and it should be particularly useful for high-throughput analyses of molecular conformations. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010

@article{Liu2009RotationMatrixOptimization, abstract = {Finding the rotational matrix that minimizes the sum of squared deviations between two vectors is an important problem in bioinformatics and crystallography. Traditional algorithms involve the inversion or decomposition of a 3 × 3 or 4 × 4 matrix, which can be computationally expensive and numerically unstable in certain cases. Here, we present a simple and robust algorithm to rapidly determine the optimal rotation using a Newton-Raphson quaternion-based method and an adjoint matrix. Our method is at least an order of magnitude more efficient than conventional inversion/decomposition methods, and it should be particularly useful for high-throughput analyses of molecular conformations. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010}, added-at = {2018-03-06T04:06:47.000+0100}, author = {Liu, Pu and Agrafiotis, Dimitris K. and Theobald, Douglas L.}, biburl = {https://www.bibsonomy.org/bibtex/2ac970a720ec31f9e166e9e1f70e196e6/degeed123}, doi = {10.1002/jcc.21439}, interhash = {f25a39a60524f09066fe67383e6fe282}, intrahash = {ac970a720ec31f9e166e9e1f70e196e6}, issn = {1096-987X}, journal = {Journal of Computational Chemistry}, keywords = {}, number = 7, pages = {1561--1563}, publisher = {Wiley Subscription Services, Inc., A Wiley Company}, timestamp = {2018-03-06T04:06:47.000+0100}, title = {Fast determination of the optimal rotational matrix for macromolecular superpositions}, url = {http://dx.doi.org/10.1002/jcc.21439}, volume = 31, year = 2010 }