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  • 1
    Digitale Medien
    Digitale Medien
    An iterative substructuring algorithm for equilibrium equations (1990)
    Springer
    Numerische Mathematik 57 (1990), S. 625-633 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10, 65N30 ; CR: G1.3, G1.8
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The topic of iterative substructuring methods, and more generally domain decomposition methods, has been extensively studied over the past few years, and the topic is well advanced with respect to first and second order elliptic problems. However, relatively little work has been done on more general constrained least squares problems (or equivalent formulations) involving equilibrium equations such as those arising, for example, in realistic structural analysis applications. The potential is good for effective use of iterative algorithms on these problems, but such methods are still far from being competitive with direct methods in industrial codes. The purpose of this paper is to investigate an order reducing, preconditioned conjugate gradient method proposed by Barlow, Nichols and Plemmons for solving problems of this type. The relationships between this method and nullspace methods, such as the force method for structures and the dual variable method for fluids, are examined. Convergence properties are discussed in relation to recent optimality results for Varga's theory ofp-cyclic SOR. We suggest a mixed approach for solving equilibrium equations, consisting of both direct reduction in the substructures and the conjugate gradient iterative algorithm to complete the computations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01386432
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  • 2
    Digitale Medien
    Digitale Medien
    Optimality relationships forp-cyclic SOR (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 635-643 
    Details
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65F10 ; CR: G 1.3
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The optimality question for blockp-cyclic SOR iterations discussed in Young and Varga is answered under natural conditions on the spectrum of the block Jacobi matrix. In particular, it is shown that repartitioning a blockp-cyclic matrix into a blockq-cyclic form,q〈p, results in asymptotically faster SOR convergence for the same amount of work per iteration. As a consequence block 2-cyclic SOR is optimal under these conditions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01405193
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  • 3
    Digitale Medien
    Digitale Medien
    Optimal $p$ --cyclic SOR (1994)
    Springer
    Numerische Mathematik 67 (1994), S. 475-490 
    Details
    ISSN: 0945-3245
    Schlagwort(e): Mathematics Subject Classification (1991): 65F10
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary. Our purpose in this paper is to extend $p$ --cyclic SOR theory to consistent singular systems and to apply the results to the solution of large scale systems arising, {\em e.g.,} in queueing network problems in Markov analysis. Markov chains and queueing models lead to structured singular linear systems and are playing an increasing role in the understanding of complex phenomena arising in computer, communication and transportation systems. For certain important classes of singular problems, we develop a convergence theory for $p$ --cyclic SOR, and show how to repartition for optimal convergence. Results by Kontovasilis, Plemmons and Stewart on the concept of convergence of SOR in an {\em extended} sense are rigorously analyzed and applied to the solution of periodic Markov chains with period $p = 2$ .
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002110050039
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  • 4
    Digitale Medien
    Digitale Medien
    Generalization of Strang's Preconditioner with Applications to Toeplitz Least Squares Problems (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 3 (1996), S. 45-64 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Toeplitz least squares problems ; circulant preconditioned conjugate gradient method ; deconvolution ; image restoration ; atmospheric imaging ; medical imaging ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we propose a method to generalize Strang's circulant preconditioner for arbitrary n-by-n matrices An. The th column of our circulant preconditioner Sn is equal to the th column of the given matrix An. Thus if An is a square Toeplitz matrix, then Sn is just the Strang circulant preconditioner. When Sn is not Hermitian, our circulant preconditioner can be defined as . This construction is similar to the forward-backward projection method used in constructing preconditioners for tomographic inversion problems in medical imaging. We show that if the matrix An has decaying coefficients away from the main diagonal, then is a good preconditioner for An. Comparisons of our preconditioner with other circulant-based preconditioners are carried out for some 1-D Toeplitz least squares problems: min ∥ b - Ax∥2. Preliminary numerical results show that our preconditioner performs quite well, in comparison to other circulant preconditioners. Promising test results are also reported for a 2-D deconvolution problem arising in ground-based atmospheric imaging.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
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  • 5
    Digitale Medien
    Digitale Medien
    Adaptive Lanczos methods for recursive condition estimation (1991)
    Springer
    Numerical algorithms 1 (1991), S. 1-19 
    Details
    ISSN: 1572-9265
    Schlagwort(e): AMS(MOS) ; 15A18 ; 65F10 ; 65F20 ; 65F35 ; Adaptive methods ; condition estimation ; control ; downdating ; eigenvalues ; Lanczos methods ; matrix modifications ; recursive least squares ; signal processing ; singular values ; updating
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Estimates for the condition number of a matrix are useful in many areas of scientific computing, including: recursive least squares computations, optimization, eigenanalysis, and general nonlinear problems solved by linearization techniques where matrix modification techniques are used. The purpose of this paper is to propose anadaptiveLanczosestimator scheme, which we callale, for tracking the condition number of the modified matrix over time. Applications to recursive least squares (RLS) computations using the covariance method with sliding data windows are considered.ale is fast for relatively smalln-parameter problems arising in RLS methods in control and signal processing, and is adaptive over time, i.e., estimates at timet are used to produce estimates at timet+1. Comparisons are made with other adaptive and non-adaptive condition estimators for recursive least squares problems. Numerical experiments are reported indicating thatale yields a very accurate recursive condition estimator.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02145580
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  • 6
    Digitale Medien
    Digitale Medien
    Tracking the condition number for RLS in signal processing (1992)
    Springer
    Mathematics of control, signals, and systems 5 (1992), S. 23-39 
    Details
    ISSN: 1435-568X
    Schlagwort(e): Adaptive algorithms ; Condition estimation ; Recursive least squares ; Signal processing ; Singular values
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Elektrotechnik, Elektronik, Nachrichtentechnik , Mathematik , Technik allgemein
    Notizen: Abstract We apply a fast adaptive condition estimation scheme, calledACE, to recursive least squares (RLS) computations in signal processing.ACE is fast in the sense that onlyO(n) operations are required forn parameter problems, and is adaptive over time, i.e., estimates at timet are used to produce estimates at timet + 1. RLS algorithms for linear prediction of time series are applied in various fields of signal processing: identification, estimation, and control. However, RLS algorithms are known to suffer from numerical instability problems under finite word-length conditions, due to ill-conditioning. We apply adaptive procedures, linear in the order of the problem, for accurately tracking relevant extreme eigen-values or singular values and the associated condition numbers over timet. In this paper exponentially weighted data windows are considered. The sliding data window case, which involves downdating as well as updating, is considered else-where. Numerical experiments indicate thatACE yields an accurate, yet inexpensive, RLS condition estimator for signal processing applications.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01211974
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