Until recently it has been impossible to accurately determine the roots of polynomials of high degree, even for polynomials derived from the Z transform of time series where the dynamic range of the coefficients is ge...
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Until recently it has been impossible to accurately determine the roots of polynomials of high degree, even for polynomials derived from the Z transform of time series where the dynamic range of the coefficients is generally less than 100 dB. In a companion paper, two new programs for solving such polynomials were discussed and applied to signature analysis of one-sided time series [1]. We present here another technique, that of root projection (RP), together with a gram-schmidt method for implementing it on vectors of large dimension. This technique utilizes the roots of the Z transform of a one-sided time series to construct a weighted least squares modification of the time series whose Z transform has an appropriately modified root distribution. Such a modification can be employed in a manner which is very useful for filtering and deconvolution applications [2]. Examples given here include the use of boundary root projection for front end noise reduction and a generalization of Prony's method.
In this paper, the parallel implementation of two algorithms for forming a QR factorization of a matrix is studied. We propose parallel algorithms for the modified gram-schmidt and the Householder algorithms on messag...
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In this paper, the parallel implementation of two algorithms for forming a QR factorization of a matrix is studied. We propose parallel algorithms for the modified gram-schmidt and the Householder algorithms on message passing systems in which the matrix is distributed by blocks or rows. The models that predict performance of the algorithms are validated by experimental results on several parallel machines.
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