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- W2945439908 abstract "We analyze effective approximation of unitary matrices. In our formulation, a unitary matrix is represented as a product of rotations in two-dimensional subspaces, so-called Givens rotations. Instead of the quadratic dimension dependence when applying a dense matrix, applying such an approximation scales with the number factors, each of which can be implemented efficiently. Consequently, in settings where an approximation is once computed and then applied many times, such a representation becomes advantageous. Although effective Givens factorization is not possible for generic unitary operators, we show that minimizing a sparsity-inducing objective with a coordinate descent algorithm on the unitary group yields good factorizations for structured matrices. Canonical applications of such a setup are orthogonal basis transforms. We demonstrate numerical results of approximating the graph Fourier transform, which is the matrix obtained when diagonalizing a graph Laplacian." @default.
- W2945439908 created "2019-05-29" @default.
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- W2945439908 date "2019-05-14" @default.
- W2945439908 modified "2023-09-27" @default.
- W2945439908 title "Approximating Orthogonal Matrices with Effective Givens Factorization" @default.
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