  In this paper, we discuss the convergence analysis of the conjugate
gradient-based algorithm for the functional linear model in the reproducing
kernel Hilbert space framework, utilizing early stopping results in
regularization against over-fitting. We establish the convergence rates
depending on the regularity condition of the slope function and the decay rate
of the eigenvalues of the operator composition of covariance and kernel
operator. Our convergence rates match the minimax rate available from the
literature.
