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This paper describes iterative procedures for determining linear and piecewise linear discriminant functions for multicategory pattern classifiers. While classifiers with the same structure have often been proposed, it is less well known that their parameters can be efficiently determined by simple adjustment procedures. For linear discriminant functions, convergence proofs are given for procedures that are guaranteed to yield error-free solutions on design samples, provided only that such solutions exist. While no similar results are known for piecewise linear discriminant functions, simple procedures are given that have been effective in various experiments. The results of experiments with artificially generated multimodal data and with hand-printed alphanumeric characters are given to show that this approach compares favorably with other classification methods.