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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.
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