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The purpose of semi-blind channel identification methods is to exploit the information used by blind methods and the information coming from known symbols. The main focus of this paper is the study of deterministic quadratic semi-blind algorithms which are of particular interest because of their low computational complexity. The associated criteria are formed as a linear combination of a blind and a training sequence based criterion. Through the examples of subchannel response matching and subspace fitting based semi-blind criteria, we study how to construct properly such semi-blind criteria and how to choose the weights of the linear combination. We provide a performance study for these algorithms and give theoretical conditions for the semi-blind performance to be independent of the weights.