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Numerical Properties of a Multivariate Ritz-Trefftz Method

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2 Author(s)
Bosarge, W.E. ; IBM Scientific Center, 6900 Fannin Street, Houston, Texas 77025, USA ; Smith, C.L.

In this paper the numerical properties of the Ritz-Trefftz algorithm are discussed in the context of the numerical approximation to the linear parabolic regulator problem using multivariate splines. The algorithm is first derived in the problem context and the resulting linear algebraic system is discussed. Such properties as definiteness and band structure are treated. The algorithm is applied to a number of sample control problems, and it is shown that the method yields efficient and highly accurate continuous approximations to the solutions of the selected sample problems. Computer implementation of the general algorithm is also discussed.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:16 ,  Issue: 4 )