Proceedings PaperWavelet approximations to Jacobians and the inversion of complicated maps
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Principal orthogonal decomposition can be used to solve two related problems: distinguishing elements from a collection by making d measurements, and inverting a complicated map from a p- parameter configuration space to a d-dimensional measurement space. In the case where d is more than 1000 or so, the classical O(d3) singular value decomposition algorithm becomes very costly, but it can be replaced with an approximate best-basis method that has complexity O(d2 log d). This can be used to compute an approximate Jacobian for a complicated map from Rp to Rd in the case where p is much less than d.