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A method is developed for providing the optimal feedback gain matrix for high-order linear quadratic problems by a decentralized computational procedure. All the calculations in this approach are done off-line. The resulting gains are optimal for all initial conditions so that the eventual on-line computation is minimal. The method is applicable to both the regulator and the servomechanism problems and is particularly attractive to use for the infinite time case where even the off-line computation is small. A 22nd-order numerical example is used to illustrate the approach. The system here is the practical one of river pollution control based on some data from the river Cam near Cambridge, England. For this case, the optimal feedback matrix is calculated using the new approach.