SVD { Updating Using Orthonormal { Rotations
نویسندگان
چکیده
In this paper the implementation of the SVD{updating algorithm using orthonormal { rotations is presented. An orthonormal {rotation is a rotation by an angle of a given set of {rotation angles (e.g. the angles i = arctan2 ?i) which are choosen such that the rotation can be implemented by a small amount of shift{add operations. A version of the SVD{updating algorithm is used where all computations are entirely based on the evaluation and application of orthonormal rotations. Therefore, in this form the SVD{updating algorithm is amenable to an implementation using orthonormal {rotations, i.e., each rotation executed in the SVD{updating algorithm will be approximated by orthonormal {rotations. For all the approximations the same accuracy is used, i.e., only r w (w: wordlength) orthonormal { rotations are used to approximate the exact rotation. The rotation evaluation can also be performed by the execution of {rotations such that the complete SVD{updating algorithm can be expressed in terms of orthonormal {rotations. Simulations show the eeciency of the SVD{updating algorithm based on orthonormal {rotations.
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