Linear Dependence Relations Connecting Equal Interval Nth Degree Splines and Their Derivatives

Present address: The Polytechnic of the South Bank, Borough Road, London, S.E.1 England. The linear dependence of the values of Nth degree spline andits pth derivatives at N successive equally spaced knots isshown and the constants associated with this linear dependencecalculated. A recurrence relation which enables the constants to be foundfor any N is also given. The results are applied to equal intervalinterpolation.