Derivation of the Optimal Solution

Let us just take the derivative of J (Eq. 1.30) with respect to the weights, using matrix operations.

NEURAL AND ADAPTIVE SYSTEMS00000194.gif

since the transpose of R is equal to itself because of its Toeplitz strucutre). If we equate this to zero, we obtain the optimal weights,

NEURAL AND ADAPTIVE SYSTEMS00000195.gif

which is the equation in the text.

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