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An algorithm for calculating the QR and singular value decompositions of polynomial matrices
Abstract
In this paper, a new algorithm for calculating the QR decomposition (QRD) of a polynomial matrix is introduced. This algorithm amounts to transforming a polynomial matrix to upper triangular form by application of a series of paraunitary matrices such as elementary delay and rotation matrices. It is shown that this algorithm can also be used to formulate the singular value decomposition (SVD) of a polynomial matrix, which essentially amounts to diagonalizing a polynomial matrix again by application of a series of paraunitary matrices. Example matrices are used to demonstrate both types of decomposition. Mathematical proofs of convergence of both decompositions are also outlined. Finally, a possible application of such decompositions in multichannel signal processing is discussed- Text
- Journal contribution
- Mechanical engineering not elsewhere classified
- Convolutive mixing
- Multiple-input–multiple-output (MIMO) channel equalization
- Paraunitary matrix
- Polynomial matrix QR decomposition (QRD)
- Polynomial matrix singular value decomposition (SVD)
- Mechanical Engineering not elsewhere classified