P. Van Dooren, "Numerical Linear Algebra Techniques for Large Scale Matrix Problems in Systems and Control," Proc. 31st Conf. Decision Control, Tucson, USA, 1992, no. TM-6.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....step further by forming Vk and W via a two sided, nonsymmetric Lanczos method [24] The Lanczos algorithm simultaneously computes the projector, r, and a tridiagonal with only O(k2n) operations. Employing the Lanczos method for model reduction is discussed in a multitude of recent papers including [1, 4, 23, 32, 33, 34]. Model reduction via a Krylov projector is certainly cheaper, O(k2n) than with an optimal reduction technique, O(n3) when n k. However, Pad approximation and more specifically Lanczos based model reduction is known to suffer from three significant disadvantages. 1. Singularities in the ....

....of the utmost importance that the unstable modes of the large scale system appear in some form in the reduced order model. The use of implicit restarts to achieve this remains an area for future research. Lanczos methods are already being applied to model reduction problems in the area of control [4, 23, 34]. However, in many applications, sparse systems occur in implicit state space systems rather than in explicit ones. In other words, instead of working with (1) and (2) the more general state space equation Eic = Ax Bu (50) y = Cx Du (51) should be treated. In this case, one must be concerned ....

P. Van Dooren, "Numerical linear algebra techniques for large scale matrix problems in systems and control," Proc. IEEE $1st Conf. on Decision and Control, (Tucson, AZ), 1992. 23

.... Lanczos method was utilized in structural dynamics for model reduction based on eigenvalue analysis [50, 51, 52] Later work in the field utilized the Lanczos method for Pad e approximation [53] including MIMO systems [54, 55] The next wave of application work took place in the control literature [56, 57, 58]. A large amount of existing work was repeated, although new results did appear in the areas of error analysis [59] and stability retention [60] Very recently, Lanczos based model reduction has become a popular topic in the area of high speed circuits. Existing Lanczos algorithms were applied to ....

P. M. Van Dooren, "Numerical linear algebra techniques for large scale matrix problems in systems and control," in Proc. 31st IEEE Conf. Decision Control, Tucson, AZ, 1992.

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P. Van Dooren, "Numerical Linear Algebra Techniques for Large Scale Matrix Problems in Systems and Control," Proc. 31st Conf. Decision Control, Tucson, USA, 1992, no. TM-6.

.... Gamma1 g Psi (8) for specific choices of G and g. The first connection between the Lanczos algorithm, a Krylov based technique, and Pad e approximations was given in [12] Later work proposed related Krylov space techniques for model reduction of dynamical systems in various application areas [19, 16, 26, 24, 4, 25]. New results in the area included stability retention of the reduced order model [13] and multipoint rational Lanczos methods [10] i.e. starting from the Lanczos procedure and modifying it to produce a reduced system that matched multiple moments at multiple frequency values. We now give a ....

P. Van Dooren (1992), Numerical linear algebra techniques for large scale matrix problems in systems and control, Proc. 31st IEEE Conf. Dec. Contr., Tucson, AZ.

....method was utilized in structural dynamics for model reduction based on eigenvalue analysis. 21, 22, 23] Later work in the field utilized the Lanczos method for Pad e approximation including 5 MIMO systems. 24, 25, 26] The next wave of application work took place in the control literature . [27, 28, 29] A large amount of existing work was repeated, although new results did appear in the areas of error analysis and stability retention. 30, 31] Very recently, Lanczos based model reduction has become a popular topic in the area of high speed circuits. Existing Lanczos algorithms were applied to ....

P. M. Van Dooren. Numerical linear algebra techniques for large scale matrix problems in systems and control. In 31st IEEE Conf. Decision Contr., Tucson, AZ, 1992.

....Software developments such as interactive packages [38] and software libraries [34] Combinations of the above issues, such as in the problem of model reduction of large sparse systems. This clearly involves sparse matrix techniques but all three other issues come up as well as e.g. indicated in [33]. Acknowledgement Part of this research was performed while visiting the Institute of Mathematics and Applications of the University of Minnesota, Minneapolis, during the summer quarter of the Applied Linear Algebra Year organized there. We greatly appreciated the hospitality and the productive ....

P. Van Dooren, Numerical linear algebra techniques for large scale matrix problems in systems and control, Proceedings 31st IEEE Conf. Dec. & Contr. (1992) to appear.

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P. Van Dooren, Numerical linear algebra techniques for large scale matrix problems in systems and control, Proc. 31st Conference on Decision and Control, Tucson, AZ, 1992.

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