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A fast algorithm for solving diagonally dominant symmetric pentadiagonal Toeplitz systems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第4期234卷 995-1005页

作者： McNally, Jeffrey Mark St Francis Xavier Univ Dept Math Stat & Comp Sci Antigonish NS B2G 2W5 Canada

Banded Toeplitz systems of linear equations arise in many application areas and have been well studied in the past. Recently, significant advancement has been made in algorithm development of fast parallel scalable methods to solve tridiagonal Toeplitz problems. In this paper we will derive a new algorithm for solving symmetric pentadiagonal Toeplitz systems of linear equations based upon a technique used in [J.M. McNally, L.E. Garey, R.E. Shaw, A split-correct parallel algorithm for solving tri-diagonal symmetric Toeplitz systems, Int. J. Comput. Math. 75 (2000) 303-313] for tridiagonal Toeplitz systems. A common example which arises in natural quintic spline problems will be used to demonstrate the algorithm's effectiveness. Finally computational results and comparisons will be presented. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Toeplitz Pentadiagonal Linear systems fast algorithm Perturbation analysis Natural quintic splines

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New fast algorithm for optimal design of block digital filters by skew-cyclic convolution

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IET SIGNAL PROCESSING 2014年第6期8卷 633-638页

作者： Fu, Deqian Jiang, Zhaolin Cui, Yifeng Jhang, Seong Tae Linyi Univ Sch Informat Linyi 276005 Peoples R China Linyi Univ Sch Sci Linyi 276005 Peoples R China Univ Suwon Coll Informat Technol Hwaseong Si 445743 Gyeonggi Do South Korea

In this study, a new fast algorithm for optimal design of block digital filters is proposed based on the skew circulant matrix, the Toeplitz and the skew shift cyclic matrices. The developed skew-cyclic filter, compared with the cyclic filter, not only achieves the same computational complexity of the design process and the memory requirements, but is more efficient with only approximately half of the computational cost for the real signals.

关键词： digital filters Toeplitz matrices fast algorithm optimal design block digital filter skew-cyclic convolution skew circulant matrix shift cyclic matrices skew-cyclic fllter Toeplitz matrices

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fast algorithm OF ARBITRARY FACTOR SUBPIXEL DOWNSAMPLING BASED ON FREQUENCY ANALYSIS

FAST ALGORITHM OF ARBITRARY FACTOR SUBPIXEL DOWNSAMPLING BAS...

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IEEE International Conference on Multimedia and Expo Workshops (ICMEW)

作者： Tang, Ketan Au, Oscar C. Fang, Lu Pang, Jiahao Guo, Yuanfang Li, Jiali Hong Kong Univ Sci & Technol Hong Kong Hong Kong Peoples R China Univ Sci & Technol China CAS Key Lab Technol Geospatial Informat Proc & Ap Hong Kong Hong Kong Peoples R China

ISBN: (纸本)9781479947614

Subpixel-based downsampling has shown its advantages over pixel-based downsampling in terms of preserving more spatial details along edges and generating sharper images, at the cost of certain amount of color-fringing artifacts in the downsampled image. To balance the sharpness and color-fringing artifacts, some algorithms are proposed to design optimal anti-aliasing (AA) filters, which are either image independent, or computationally too expensive. And all of the existing AA filters are designed for fixed downsampling factor, which makes them impractical for real applications. In this paper we propose two fast algorithms to design AA filter for arbitrary factor subpixel downsampling based on frequency analysis of the input image. The proposed algorithms generate image dependent AA filter which is as good as the state-of-the-art algorithm, but much faster.

关键词： subpixel-based downsampling arbitrary factor fast algorithm frequency analysis

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A physics-based fast algorithm for structural responses of generalized rotationally axisymmetric structures: the generalized rotation-superposition method

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LATIN AMERICAN JOURNAL OF SOLIDS AND STRUCTURES 2024年第6期21卷 1-22页

作者： Yang, Mao Zhang, Jun Chen, Hao Yang, Jialin Mao, Yongjian China Acad Engn Phys Inst Syst Engn Mianyang 621999 Sichuan Peoples R China

fast calculations are widely required in the traditional applications and the emerging digital twin fields. For those considerations, a novel physics-based fast algorithm, namely generalized rotation-superposition method, is proposed for fast calculating linear elastic responses of generalized rotationally axisymmetric structures under arbitrary mechanical loads. This improved method breaks through the limitations of the previous basic rotationsuperposition method in rotational similarity of load and structural axisymmetry, and greatly expands its application scope. In this paper, firstly, the basic theory of the rotation-superposition algorithm is introduced;secondly, the theoretical model of the generalized rotation-superposition method is established;thirdly, the effectiveness and accuracy are verified by using finite element simulations;finally, through a complex case study, the applicability of the generalized rotation-superposition method for complex engineering problems and its advantages in efficiently obtaining massive amounts of data are further illustrated.

关键词： fast algorithm structural response axisymmetric structure rotationally axisymmetric structure rotation-superposition method digital twin

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Robust and fast algorithm for estimating fundamental periodicity of jet engine modulation signals

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IET RADAR SONAR AND NAVIGATION 2016年第7期10卷 1286-1294页

作者： Yong, Yang Woo Hoon, Park Ji Young, Song Won Hoon, Myung Noh Hanwha Thales Radar Res Ctr Seoul South Korea Agcy Def Dev Technol Ctr POB 35-3 Yuseong Daejeon South Korea Korea Adv Inst Sci & Technol Dept Elect Engn 335 Gwahangno Daejeon 305701 South Korea

Jet engine modulation (JEM), a modulation phenomenon induced by a rotating jet engine compressor, is a representative feature extracted from the radar for aircraft target recognition. In this study, the authors present a robust and fast algorithm for extracting the spool rate, which imparts fundamental periodicity to JEM signals. First, a wavelet decomposition with Meyer wavelet was applied to the analytic form of the JEM signal. Then, the decomposition components were combined to achieve a sufficient energy and minimise the mean of the JEM auto-correlation. Finally, the peak detection algorithm was employed for automatic estimation of the spool rate. Application results of measured JEM signals demonstrated that the proposed algorithm is effective for stable and accurate extraction of the jet engine information.

关键词： object recognition radar detection wavelet transforms feature extraction correlation methods jet engines radar target recognition compressors automatic spool rate estimation peak detection algorithm JEM auto-correlation decomposition components Meyer wavelet wavelet decomposition JEM signals spool rate extraction aircraft target recognition representative feature extraction rotating jet engine compressor jet engine modulation signals fundamental periodicity estimation fast algorithm robust algorithm

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A fast algorithm for computing multidimensional DCT on certain small sizes

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2003年第1期51卷 213-220页

作者： Chen, XJ Dai, QH Li, CW Tsing Hua Univ Dept Automat Beijing Peoples R China

This paper presents a new algorithm for the fast computation of multidimensional (m-D) discrete cosine transform (DCT) with size N-1 x N-2 x (...) x N-m, where N-i is a power of 2 and N-1 less than or equal to 256, by using the tensor product decomposition of the transform matrix. It is shown that the m-D DCT or inverse discrete cosine transform (IDCT) on these small sizes can be computed using only one-dimensional (1-D) DCTs and additions and shifts. If all the dimensional sizes are the same, the total number of multiplications required for the algorithm is only 1/m times of that required for the conventional row-column method. We also introduce approaches for computing scaled DCTs in which the number of-multiplications is considerably reduced.

关键词： discrete cosine transform fast algorithm permutation matrix tensor product

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Exact and fast algorithm for two-dimensional image wavelet moments via the projection transform

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PATTERN RECOGNITION 2005年第3期38卷 395-402页

作者： Pan, H Xia, LZ SE Univ Dept Automat Control Engn Nanjing 210096 Peoples R China Hong Kong Polytech Univ Dept Elect & Informat Engn Hong Kong Hong Kong Peoples R China

Wavelet moments are perfect representations of moments in multiresolution wavelet domain, which integrates the theory of moment invariants into wavelet analysis. However, the calculations of moments are very complicated in terms of computational complexity, so it is difficult to implement them in real time. An exact and fast projection-based algorithm for two-dimensional wavelet moments is presented in this paper. In our approach, the computation of a two-dimensional wavelet moment of order of r is performed in (r + 1) different one-dimensional spaces. Since only additions are required to perform the projection transform, the total computational complexity can be greatly reduced. CO 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.

关键词： wavelet transform multiresolution analysis moment fast algorithm

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A fast algorithm for Computation of Electromagnetic Wave Propagation in Half-Space

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2009年第7期57卷 2068-2075页

作者： Liao, Shaolin Vernon, Ronald J. Univ Wisconsin Dept Elect & Comp Engn Madison WI 53706 USA

A new frequency-domain algorithm, the planar Taylor expansion through the fast Fourier transform (FFT) method, has been developed to speed the computation of the Green's function related formulas in the half-space scenario for both the near-field (NF) and the far-field (FF). Two types of Taylor-FFT algorithms are presented in this paper: the spatial Taylor-FFT and the spectral Taylor-FFT. The former is for the computation of the NF and the latter is for the computation of the FF or the Fourier spectrum. The planar Taylor-FFT algorithm has a computational complexity of O(N-2 log(2) N-2) for an N x N computational grid, comparable to the multilevel fast multipole method (MLFMM). What's more important is that, the narrowband property of many electromagnetic fields allows the Taylor-FFT algorithm to use larger sampling spacing, which is limited by the transverse wave number. In addition, the algorithm is free of singularities. An accuracy of -50 dB for the planar Taylor-FFT algorithm is easily obtained and an accuracy of -80 dB is possible when the algorithm is optimized. The algorithm works particularly well for narrowband fields and quasi-planar geometries.

关键词： fast algorithm fast Fourier transform (FFT) Green's Function multilevel fast multipole method (MLFMM)

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A fast algorithm for Fractional QCQP and Applications to Secure Beamforming in Cognitive Nonorthogonal Multiple Access Networks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2021年 69卷 6237-6250页

作者： Luo, Hualiang Li, Quanzhong Yang, Liang Qin, Jiayin Sun Yat Sen Univ Sch Elect & Informat Technol Guangzhou 510006 Peoples R China Sun Yat Sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Hunan Univ Coll Comp Sci & Elect Engn Changsha 410082 Hunan Peoples R China

In this paper, we investigate a nonconvex fractional quadratically constrained quadratic problem (fractional QCQP), which has a wide application to the resource allocation optimization in wireless communication systems. Different from the state-of-the-art methods needing to solve semidefinite programmings or second-order cone programmings, we propose a fast algorithm for solving fractional QCQP by combining the successive convex approximation method and the consensus alternating direction method of multipliers, which has only simple computations and works very fast in applications with modest accuracy. We also apply the proposed fast algorithm to secure beamforming design for enhancing physical layer security in cognitive nonorthogonal multiple access (NOMA) networks, where secrecy rate optimization problems in both underlay and overly cognitive NOMA networks are typical fractional QCQPs and have not been well studied. Simulation results have shown that our proposed fast algorithm achieves almost the same performance as the state-of-the-art methods, however, the proposed fast algorithm has very low computation complexity.

关键词： NOMA Signal processing algorithms Optimization Array signal processing Programming Resource management Multicast communication Fractional quadratically constrained quadratic problem (Fractional QCQP) fast algorithm secure beamforming cognitive radios nonorthogonal multiple access

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A new fast algorithm to compute moment 3D invariants of generalized Laguerre modified by fractional-order for pattern recognition

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MULTIDIMENSIONAL SYSTEMS AND SIGNAL PROCESSING 2021年第2期32卷 431-464页

作者： El Ogri, O. Karmouni, H. Yamni, M. Daoui, A. Sayyouri, M. Qjidaa, H. Univ Sidi Mohamed Ben Abdellah Fac Sci Dhar El Mahrez Lab Elect Signals & Syst Informat LESSI CED STSTIC Fes Morocco Sidi Mohamed Ben Abdellah Univ Natl Sch Appl Sci Engn Syst & Applicat Lab BP 72My Abdallah AveKm 5Imouzzer Rd Fes Morocco

Orthogonal moments are the projections of image functions on particular functions of the kernel. They play an essential role in image extraction: rotation, scaling, translation invariance, object recognition, image classification, image noise robustness, and low information redundancy. These moments are derived from orthogonal polynomials that can be continuous or discrete. This paper focuses on the fractional-order modified generalized Laguerre moment invariants (FMGLMIs), which is a generalization of the traditional integer order one. In this research, we have developed a new algorithm to compute the 3D invariant moments of FMGLMIs based on the 3D image cuboid representation, our proposed calculation method can improve the efficiency of 3D invariant moment calculation to maintain numerical stability and significantly reduce calculation time with very satisfactory accuracy. To check this new algorithm, the calculation of 3D invariant moments gives very encouraging results for the invariability property of the proposed method with respect to different geometric transformations and noise degradations of 3D images, classification and recognition of 3D images and the calculation time of fractional-order invariants proposed. Finally, the experimental results show that the proposed method makes it possible to construct fractional-order modified generalized Laguerre invariant moments offering better performances for image analysis and pattern recognition.

关键词： Fractional-order modified generalized Laguerre polynomials Fractional-order moment Invariants fast algorithm Accurate computation 3D image classification Pattern recognition

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