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Exact(11)
The QR decomposition and the matrix inversion can be performed only once over the frame.
Since we are limited to a MIMO system, the matrix inversion can be calculated directly using Cramer's rule, where denotes the adjoint of the matrix.
While the latter is certainly not the case, by this assumption a costly matrix inversion can be avoided at the expense of some accuracy.
1 Matrix multiplication combined with matrix inversion can be implemented using the Strassen's algorithm in [40] and the improved Coppersmith-Winograd algorithm in [41].
The optimal solution to (35) with matrix inversion can be denoted by w l = R ^ l - 1 Vec S t l Vec H S t l R ^ l - 1 Vec S t l. (37).
The LS solution requires the inversion of the (mathcal {T}times mathcal {T}) matrix R, and the computational cost of the matrix inversion can be high when (mathcal {T}) is large.
Similar(49)
To determine the inverse of (hat {mathbf {R}}_{2}(n)), the block-matrix inversion can be used.
The approach is shown in next subsection, where we show that Jacobian matrix (6) of static QNU can be calculated only once and that also the matrix inversion (5) can be avoided for QNU (Section 3.5).
The p-algorithm does not involve matrix inversion and can be implemented in two ways: FFT-based search and polynomial rooting [5].
Because Chebyshev filter diagonalization avoids the need for matrix inversion it can deal with matrices and problem sizes that are presently not accessible with rational function methods based on direct or iterative linear solvers.
By using matrix inversion lemma, we can get (50).
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