Applications of geometric algebra to the theory of molecular conformation: Part 1. The optimum alignment problem

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Geometric algebra is an elegant and practical merger of classical vector algebra with Hamilton's quaternions. As part of our ongoing studies of its many potential applications to the theory of molecular conformation, we show how geometric algebra can be used to characterize the solutions to the classical problem of computing the optimum alignment of rigid structures. Using this characterization, we derive a new iterative algorithm for finding optimum alignments, which we can show is both globally and quadratically convergent.