Good Rotations
نویسندگان
چکیده
منابع مشابه
Good Rotations
Numerical integrations in celestial mechanics often involve the repeated computation of a rotation with a constant angle. A direct evaluation of these rotations yields a linear drift of the distance to the origin. This is due to roundoff in the representation of the sine s and cosine c of the angle θ. In a computer, one generally gets c 2 + s 2 = 1, resulting in a mapping that is slightly contr...
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We describe online algorithms for learning a rotation from pairs of unit vectors in R. We show that the expected regret of our online algorithm compared to the best fixed rotation chosen offline over T iterations is O( √ nT ). We also give a lower bound that proves that this expected regret bound is optimal within a constant factor. This resolves an open problem posed in COLT 2008. Our online a...
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Suppose A1, . . . , AN are rotation matrices on n-dimensional Euclidean space R, i.e., Aj ∈ SO(n). We want to consider some element of SO(n) that represents an “average” of these elements Aj . There are a number of possible ways to define the notion of an average in this context. One approach has been to write Aj = ej with Zj a real, skew-symmetric n × n matrix (i.e., Zj ∈ skew(n)), and define ...
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ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 1998
ISSN: 0021-9991
DOI: 10.1006/jcph.1998.6066