QR decomposition is extensively adopted in multiple-input-multiple-output orthogonal frequency-division multiplexing wireless communication systems, and is one of the performance bottlenecks in lots of high-performanc...
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QR decomposition is extensively adopted in multiple-input-multiple-output orthogonal frequency-division multiplexing wireless communication systems, and is one of the performance bottlenecks in lots of high-performance wireless communication algorithms. To implement low processing latency QR decomposition with hardware, the authors propose a novel iterative look-ahead modifiedgram-schmidt (ILMGS) algorithm based on the traditional modifiedgram-schmidt (MGS) algorithm. They also design the corresponding triangular systolic array (TSA) architecture with the proposed ILMGS algorithm, which only needs n time slots for a n x n real matrix. For reducing the hardware overhead, they modify the TSA architecture into an iterative architecture. They also design a modified iterative architecture to further reduce the hardware overhead. The implementation results show that the normalised processing latency of the modified iterative architecture based on the proposed ILMGS algorithm is 1.36 times lower than the one based on the MGS algorithm. To the best of the authors' knowledge, the designed architecture achieves the superior latency performance than the existing works.
Generating orthonormal Laguerre- Gaussian-power-like eigenvectors of the symmetric kernel matrix T of the discrete Hankel transform ( DHT) is the cornerstone in developing the discrete fractional Hankel transform (DFR...
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ISBN:
(纸本)9798350387186;9798350387179
Generating orthonormal Laguerre- Gaussian-power-like eigenvectors of the symmetric kernel matrix T of the discrete Hankel transform ( DHT) is the cornerstone in developing the discrete fractional Hankel transform (DFRHT). The direct sequential generation of the columns of each partition of the modal matrix of matrix T pertaining to one distinct eigenvalue is considered. The focus of the research is the assessment of the direct sequential algorithms: the gram-schmidtalgorithm (GSA), modified gram-schmidt algorithm (MGSA), sequential orthogonal procrustes algorithm (SOPA) and direct sequential evaluation by constrained optimization algorithm (DSEOA). Although the four algorithms are theoretically equivalent, they are quite numerically distinct. The difference in performance becomes more pronounced as the order of the square matrix T becomes larger. The assessment shows that the MGSA outperforms both the GSA and the SOPA and that the DSEOA is by far the best in terms of computation accuracy.
This paper develops a modified preconditioned conjugate gradient (M-PCG) method for moving force identification (MFI) by improving the conjugate gradient (CG) and preconditioned conjugate gradient (PCG) methods with a...
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This paper develops a modified preconditioned conjugate gradient (M-PCG) method for moving force identification (MFI) by improving the conjugate gradient (CG) and preconditioned conjugate gradient (PCG) methods with a modified gram-schmidt algorithm. The method aims to obtain more accurate and more efficient identification results from the responses of bridge deck caused by vehicles passing by, which are known to be sensitive to ill-posed problems that exist in the inverse problem. A simply supported beam model with biaxial time-varying forces is used to generate numerical simulations with various analysis scenarios to assess the effectiveness of the method. Evaluation results show that regularization matrix L and number of iterations j are very important influence factors to identification accuracy and noise immunity of M-PCG. Compared with the conventional counterpart SVD embedded in the time domain method (TDM) and the standard form of CG, the M-PCG with proper regularization matrix has many advantages such as better adaptability and more robust to ill-posed problems. More importantly, it is shown that the average optimal numbers of iterations of M-PCG can be reduced by more than 70% compared with PCG and this apparently makes M-PCG a preferred choice for field MFI applications. (C) 2017 Elsevier Ltd. All rights reserved.
This note is devoted to the rounding error analysis of the second-order Arnoldi process for constructing an orthonormal basis of the second-order Krylov subspace. The effect of the rounding errors on the orthogonality...
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This note is devoted to the rounding error analysis of the second-order Arnoldi process for constructing an orthonormal basis of the second-order Krylov subspace. The effect of the rounding errors on the orthogonality of the derived vectors is given.
This paper presents fuzzy identification of two bioprocesses employing TSK-type models. A “modifiedgram-schmidt” (MGS) orthogonal estimator is used to estimate the consequent parameters. This approach is then appli...
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This paper presents fuzzy identification of two bioprocesses employing TSK-type models. A “modifiedgram-schmidt” (MGS) orthogonal estimator is used to estimate the consequent parameters. This approach is then applied to identify two distinct cases involving dissolved oxygen concentration: one related to a bioreactor and the other one related to an activated sludge process. The obtained models are then cross-validated.
A new algorithm for downdating a QR decomposition is presented. We show that, when the columns in the Q factor from the modifiedgram-schmidt QR decomposition of a matrix X are exactly orthonormal, the gram-schmidt do...
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A new algorithm for downdating a QR decomposition is presented. We show that, when the columns in the Q factor from the modifiedgram-schmidt QR decomposition of a matrix X are exactly orthonormal, the gram-schmidt downdating algorithm for the QR decomposition of X is equivalent to downdating the full Householder QR decomposition of the matrix X augmented by an n x n zero matrix on top. Using this relation, we derive an algorithm that improves the gram-schmidt downdating algorithm when the columns in the Q factor are not orthonormal. Numerical test results show that the new algorithm produces far more accurate results than the gram-schmidt downdating algorithm far certain ill-conditioned problems.
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