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The real-time processing of the recursive least-square algorithm is difficult to execute by the conventional Neumann-type processor because of its large computational complexity. On the other hand, it is known that the recursive least-square algorithm based on the UD decomposition, which is equivalent to the recursive least-square algorithm, can be realized by the systolic array proposed by Rung. The systolic array to execute this algorithm is difficult to realize since it requires a tremendous number of elements and corrections. In the construction of the dedicated hardware, in general, the word length of the processor affects the processing speed and the hardware area. From such a viewpoint, it is important in the construction of the systolic array to execute the recursive least-square algorithm based on the UD decomposition that the word length of the processor should be minimized. To evaluate the word length, an error analysis is required for the finite word length operation of the recursive least-square algorithm based on the UD decomposition. This paper presents the finite word length floating-point error analysis for the recursive least-square algorithm, based on the UD decomposition, and evaluates the operation error. Then the convergence of the algorithm and the number of updates of the algorithm are evaluated analytically. Finally, by a computer simulation, the validity of the theoretical analysis for the convergence and the number of updates is verified. [ABSTRACT FROM AUTHOR]