New Bounds on the Zeros of Spline Functions Original Research Article

We show that, subject to a certain condition, the number of zeros of a spline function is bounded by the number of strong sign changes in its sequence of B-spline coefficients. By writing a general spline function as a sum of functions which satisfy the given condition, we can deduce known bounds on zeros and sign changes and can show that the number of zeros of any spline function is bounded by the number of weak sign changes in its sequence of B-spline coefficients, where the zero count is stronger than that previously used.