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Inverse scattering experiments, structured matrix inequalities, and tensor algebra

LINEAR ALGEBRA AND ITS APPLICATIONS 2002年 343卷 147-169页

作者： Constantinescu, T Sayed, AH Kailath, T Univ Texas Dept Math Richardson TX 75083 USA Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA

This paper deals with a general matrix extension problem with structural constraints and provides a recursive solution in terms of an inverse scattering experiment. Both the stationary and nonstationary cases are cons... 详细信息

关键词： scattering displacement structure schur algorithm matrix extension matrix inequality tensor algebra

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Square roots of 3 x 3 matrices

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CALCOLO 2017年第3期54卷 643-656页

作者： Ashkartizabi, Mehdi Aminghafari, Mina Mohammadpour, Adel Amirkabir Univ Technol Tehran Polytech Fac Math & Comp Sci Dept Stat 424 Hafez Ave Tehran 15914 Iran

We find square roots of a complex-valued matrix using equation . The proposed method is faster than Higham's method and provides up to 8 square roots with less relative residual and error.

关键词： schur algorithm Square roots Cayley-Hamilton theorem

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Regularization of the indefinite Stieltjes moment problem

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LINEAR ALGEBRA AND ITS APPLICATIONS 2020年第0期594卷 1-28页

作者： Kovalyov, Ivan Dragomanov Natl Pedag Univ Dept Math Pirogova 9 UA-01601 Kiev Ukraine

A not regular indefinite Stieltjes moment problem is studied in the generalized Stieltjes class N-k(k).The new class of the sequence s = {s(i)}(i=0)(l) is defined, which is called alpha-regular class. Regularization of the indefinite Stieltjes moment problem is obtained. The set of solutions of this problem is found in terms of the generalized Stieltjes polynomials and S-fractions with the shift alpha. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Indefinite Stieltjes moment problem Generalized Stieltjes function Generalized Stieltjes polynomials schur algorithm Resolvent matrix Continued fraction

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ROBUST H-INFINITY IDENTIFICATION OF LINEAR PERIODIC DISCRETE-TIME-SYSTEMS

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 1994年第4期4卷 595-612页

作者： ARAMBEL, PO TADMOR, G NORTHEASTERN UNIV DEPT ELECT & COMP ENGNBOSTONMA 02115

System identification algorithms for linear time-invariant (LTI) systems have been developed recently, which provide induced norm bounds on the difference between the true system and the identified one. The error bounds then allow the use of robust control design techniques with guarantees on performance of the real system. This note concerns the adaptation of robust H(infinity) identification techniques to linear periodic discrete-time (LPDT) systems. The paper focuses on the algorithm proposed by Helmicki et al. 13 and is based on a frequency-domain approach to LPDT systems.

关键词： ROBUST IDENTIFICATION PERIODIC SYSTEMS schur algorithm H-INFINITY BOUNDS

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Comparative study of joint-detection techniques for TD-CDMA based mobile radio systems

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2001年第8期19卷 1461-1475页

作者： Vollmer, M Haardt, M Götze, J Siemens AG Informat & Commun Mobile D-81359 Munich Germany Univ Dortmund Informat Proc Lab D-44221 Dortmund Germany Siemens AG Informat & Commun Mobile D-81359 Munich Germany

Third-generation mobile radio systems use time division-code division multiple access (TD-CDMA) in their time division duplex (TDD) mode. Due to the time division multiple access (TDMA) component of TD-CDMA, joint (or multi-user) detection techniques can be implemented with a reasonable complexity. Therefore, joint detection will already be implemented in the first phase of the system deployment to eliminate the intracell interference. In a TD-CDMA mobile radio system, joint-detection is performed by solving a least squares problem, where the system matrix has a block-Sylvester structure. In this paper, we present and compare several techniques that reduce the computational complexity of the joint detection task even further by exploiting this block-Sylvester structure and by incorporating different approximations. These techniques are based on the Cholesky factorization, the Levinson algorithm, the schur algorithm, and on Fourier techniques, respectively. The focus of this paper Is on Fourier techniques since they have the smallest computational complexity and achieve the same performance as the joint detection algorithm that does not use any approximations. Similar to the well-known implementation of fast convolutions, the resulting Fourier-based joint detection scheme also uses a sequence of fast Fourier transforms (FFTs) and overlapping. It is well suited for the implementation on parallel hardware architectures.

关键词： Cholesky factor fast Fourier transform joint detection Levinson algorithm overlap save schur algorithm TD-CDMA Toeplitz structure

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A FAST algorithm FOR COMPUTING MACAULAY NULL SPACES OF BIVARIATE POLYNOMIAL SYSTEMS

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2024年第1期45卷 368-396页

作者： Govindarajan, Nithin Widdershoven, Raphael Chandrasekaran, Shivkumar De Lathauwer, Lieven Dept Elect Engn SATKU Leuven B-3001 Leuven Belgium Univ Calif Santa Barbara Elect & Comp Engn Santa Barbara CA 93106 USA

As a crucial first step towards finding the (approximate) common roots of a (possibly overdetermined) bivariate polynomial system of equations, the problem of determining an explicit numerical basis for the right null space of the system's Macaulay matrix is considered. If d\Sigma \in N denotes the total degree of the bivariate polynomials of the system, the cost of computing a null space basis containing all system roots is O(d(Sigma)(6)) floating point operations through standard numerical algebra techniques (e.g., a singular value decomposition, rank-revealing QR-decomposition). We show that it is actually possible to design an algorithm that reduces the complexity to O(d(Sigma)(5)). The proposed algorithm exploits the Toeplitz structures of the Macaulay matrix under a nongraded lexicographic ordering of its entries and uses the low displacement rank properties to efficiently convert it into a Cauchy-like matrix with the help of fast Fourier transforms. By modifying the classical schur algorithm with total pivoting for Cauchy-like matrices, a compact representation of the right null space is eventually obtained from a rank-revealing LU-factorization. Details of the proposed method, including numerical experiments, are fully provided for the case wherein the polynomials are expressed in the monomial basis. Furthermore, it is shown that an analogous fast algorithm can also be formulated for polynomial systems expressed in the Chebyshev basis.

关键词： Macaulay matrices polynomials systems rank-revealing LU-factorizations low displacement rank matrices schur algorithm

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Computing the square roots of matrices with central symmetry

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APPLIED MATHEMATICS AND COMPUTATION 2007年第1期186卷 715-726页

作者： Liu, Zhongyun Zhang, Yulin Rui Ralha Changsha Univ Sci & Technol Sch Math & Comp Sci Changsha 410076 Hunan Peoples R China Univ Minho Dept Math P-4710057 Braga Portugal

For computing square roots of a nonsingular matrix A, which are functions of A, two well known fast and stable algorithms, which are based on the schur decomposition of A, were proposed by Bjork and Hammarling [A. Bjork, S. Hammarling, A schur method for the square root of a matrix, Linear Alg. Appl. 52/53 (1983) 127-140], for square roots of general complex matrices, and by Higham [N.J. Higham, Computing real square roots of a real matrix, Linear Alg. Appl. 88/89 (1987) 405-430], for real square roots of real matrices. In this paper we further consider (the computation of) the square roots of matrices with central symmetry. We first investigate the structure of the square roots of these matrices and then develop several algorithms for computing the square roots. We show that our algorithms ensure significant savings in computational costs as compared to the use of standard algorithms for arbitrary matrices. (c) 2006 Elsevier Inc. All rights reserved.

关键词： matrix square root schur algorithm central symmetry

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Design and Chip Implementation of a SMI/MVDR Dual-Mode Beamformer for Wireless MIMO Communication Systems

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IEEE ACCESS 2020年 8卷 67940-67954页

作者： Chen, Kuan-Ting Hwang, Yin-Tsung Huang, Cheng-Yi Natl Chung Hsing Univ Dept Elect Engn Taichung 40227 Taiwan MediaTek Inc Div Comp & Artificial Intelligence Hsinchu 30078 Taiwan

This paper presents a low complexity chip design supporting dual-mode beamforming, i.e. sampling matrix inversion (SMI) and the minimum variance distortionless response (MVDR), for wireless Multiple-Input Multiple-Output (MIMO) communication systems. The auto-correlation matrix inversion is the critical computing kernel shared by the two beamforming schemes. To alleviate the computing complexity, the auto-correlation matrix is approximated by a Toeplitz counterpart, which can be decomposed efficiently by applying the Cholesky decomposition and the schur algorithm. This leads to an complexity reduction, where is the matrix size, while preserving computing parallelism for the hardware design. In addition, a diagonal loading technique is employed to mitigate the stability problem when the matrix is ill-conditioned. Simulation results indicate that no performance loss is observed due to the algorithm simplification measures. A systolic array based mapping procedure converts the two beamforming algorithms to a unified hardware accelerator design with 80 & x0025;shared circuitry. Complex-valued divisions are achieved by adopting a hardware efficient coordinate rotation digital computer (CORDIC) scheme. In chip implementation, a TSMC 90nm UTM process technology is used and the design specs largely follow the requirements of IEEE 802.11ac standard. The core size of the chip design is 0.68mm(2). The measurement results show that the chip can operate up to 200MHz with a power consumption of 49.03mW. It can complete the computation of a new beamforming vector (of size 8) every 0.64us and exhibits the highest throughput among the 6 compared designs.

关键词： Array signal processing Matrix decomposition Complexity theory Matrix converters Correlation Signal processing algorithms Hardware Adaptive beamforming Cholesky decomposition schur algorithm systolic array hardware accelerator chip design

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ON GEOMETRIC SEQUENCES OF REFLECTION COEFFICIENTS AND GAUSSIAN AUTOCORRELATIONS

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PROCEEDINGS OF THE IEEE 1988年第10期76卷 1372-1374页

作者： YAGLE, AE Dept. of Electr. Eng. & Comput. Sci. Michigan Univ. Ann Arbor MI

The author shows that by interpreting the lattice filter as a discrete transmission line, the problem of determining the reflection coefficients associated with a Gaussian autocorrelation can be solved easily using the schur algorithm. These reflection coefficients have been shown to be in geometric progression; it is claimed that this has been done in a much simpler and more enlightening manner than in the presentation of G. Jacoriti and G. Scarano (see ibid., vol.75, no.7, p.960-961, 1987). The geometric progression of reflection coefficients leads to a stationarity property of the discrete transmission line, which accounts for the striking simplicity of the expressions for the waves traveling in the line

关键词： Gaussian autocorrelations schur algorithm discrete transmission line filtering and prediction theory geometric sequences lattice filter reflection coefficients stationarity property transmission line theory

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FAST SUBSPACE-BASED SYSTEM-IDENTIFICATION - AN INSTRUMENTAL VARIABLE APPROACH

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AUTOMATICA 1995年第6期31卷 903-905页

作者： CHO, YM KAILATH, T Information Systems Laboratory Stanford University Stanford CA 94305-4055 U.S.A.

Recently developed subspace-based system identification (4SID) techniques have opened new routes to the identification of multi-input multi-output systems. The 4SID techniques guarantee convergence, and run faster than the statistically efficient prediction error methods without much performance loss. The resulting computational load of the 4SID techniques is O(NM(2)), where N is the data length and M is the sliding window size. However, the computational burden O(NM(2)) can become prohibitively large as N and M grow large. Noting that the major bottleneck comes from the QR factorization of an M X N data matrix and that the existing 4SID techniques do not exploit the structure of the matrices arising in the identification procedure, we propose a new implementation of the existing 4SID, which reduces the computational burden to O(NM) by exploiting the displacement and low-rank structure of the matrices.

关键词： SUBSPACE SYSTEM IDENTIFICATION INSTRUMENTAL VARIABLE DISPLACEMENT STRUCTURE schur algorithm LANCZOS algorithm

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