On Error Bounds for a Pseudo-Formal Linearization of Chebyshev Interpolation Type

抄録

This paper is concerned with the error bounds of a pseudo-formal linearization method based on Chebyshev interpolation for nonlinear dynamic systems. First, an error bound formula is derived for a functional approximation of this linearization, in which a min-max theory is well applied to it. Then, by using this formula, another error bound formula for nonlinear dynamic systems is nicely obtained. They are more specific formulas than the general error bounds of polynomials type. Numerical experiments demonstrate the usefulness of these formulas.