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A computational method of the formal linearization for time-variant nonlinear systems by using the cubic Hermite interpolation is proposed. We introduce a linearizing function that consists of the state variables, their squares, and the cubes. The nonlinear terms are approximated by the cubic Hermite interpolation and thus a formal linear time-variant system with respect to the linearizing function is acquired. The execution of this method is easily carried out by simple matrix multiplications. A nonlinear observer and a nonlinear filter are synthesized as applications of this method and are verified through numerical examples.