How to prove that a preconditioner cannot be superlinear
Mathematics of Computation
MIMO radar waveform design via alternating projection
IEEE Transactions on Signal Processing
Tensor ranks for the inversion of tensor-product binomials
Journal of Computational and Applied Mathematics
Approximation of $2^d\times2^d$ Matrices Using Tensor Decomposition
SIAM Journal on Matrix Analysis and Applications
Information Sciences: an International Journal
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This paper considers the problem of finding n × n matrices Ak and Bk that minimize $||T - \sum A_k \otimes B_k||_F$, where $\otimes$ denotes Kronecker product and T is a banded n × n block Toeplitz matrix with banded n × n Toeplitz blocks. It is shown that the optimal Ak and Bk are banded Toeplitz matrices, and an efficient algorithm for computing the approximation is provided. An image restoration problem from the Hubble Space Telescope (HST) is used to illustrate the effectiveness of an approximate SVD preconditioner constructed from the Kronecker product decomposition.