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- W2036702685 abstract "We consider exponentially weighted recursive least squares (RLS) computations with forgetting factor γ (0 < γ < 1). The least squares estimator can be found by solving a matrix system A ( t ) x ( t ) = b ( t ) at each adaptive time step t . Unlike the sliding window RLS computation, the matrix A ( t ) is not a “near-Toeplitz” matrix (a sum of products of Toeplitz matrices). However, we show that its scaled matrix is a “near-Toeplitz” matrix, and hence the matrix-vector multiplication can be performed efficiently by using fast Fourier transforms (FFTs). We apply the FFT-based preconditioned conjugate gradient method to solve such systems. When the input stochastic process is stationary, we prove that both E [∥ A ( t ) − E ( A ( t ))∥ 2 ] and Var[∥ A ( t ) − E ( A ( t ))∥ 2 ] tend to zero, provided that the number of data samples taken is sufficient large. Here E (·) and Var(·) are the expectation and variance operators respectively. Hence the expected values of the eigenvalues of the preconditioned matrices are near to 1 except for a finite number of outlying eigenvalues. The result is stronger than those proved by Ng, Chan, and Plemmons that the spectra of the preconditioned matrices are clustered around 1 with probability 1." @default.
- W2036702685 created "2016-06-24" @default.
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- W2036702685 date "1997-09-01" @default.
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- W2036702685 title "FFT-based exponentially weighted recursive least squares computations" @default.
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- W2036702685 doi "https://doi.org/10.1016/s0024-3795(96)00532-0" @default.
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