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A new method is described in the paper to predict the reflection coefficient of a complete large log-periodic array (with large number of elements) from the computed performance of a small part of the array. The small part is referred to as the partial array. The method involves computing the embedded S-parameters between all the elements of this partial array and then using these S-parameters to predict the performance of the full array. As an example, the method has been applied to optimize the Eleven antenna for 2-13 GHz. The result of the optimization is that the reflection coefficient is improved significantly to be below -10 dB over the whole frequency band. The results have been verified by measurements.