Digital computers are built out of circuits that have definite, discrete states: on or off, zero or one, high voltage or low voltage. Engineers go to great lengths to make sure these circuits never settle into some intermediate condition. Quantum-mechanical systems, as it happens, offer a guarantee of discreteness without any engineering effort at all. When you measure the spin orientation of a...

A square-root-free matrix QR decomposition (QRD) scheme was rederived in [1] based on [2] to simplify computations when solving least-squares (LS) problems on embedded systems. The scheme of [1] aims at eliminating both the square-root and division operations in the QRD normalization and backward substitution steps in the LS computations. It is claimed in [1] that the LS solution only requires ...

We investigate the problem of linear estimation unknown mathematical expectations based on observations realizations random matrix sequences. Constructive methods have been developed for finding guaranteed RMS estimates non-stationary parameters average values It is shown that such are obtained either as solutions to boundary value problems systems differential equations or corresponding Cauchy...

Any nonsingular matrix has pth roots. One way to compute matrix pth roots is via a specialized version of Newton’s method, but this iteration has poor convergence and stability properties in general. A Schur algorithm for computing a matrix pth root that generalizes methods of Björck and Hammarling [Linear Algebra Appl., 52/53 (1983), pp. 127–140] and Higham [Linear Algebra Appl., 88/89 (1987),...

By Hermitian mapping, we suggest unitary cyclic root-MUSIC algorithm to exploit the signal selective property of cyclostationary signals in this paper. To deal with correlated or coherent case, we design the forward backward cyclic autocorrelation matrix, without conjugate centrosymmetric array configurations. Compared with unitary root-MUSIC algorithm, the proposed method has a better performa...