A unified approach to interpolation and graduation

Summary The subject of interpolation and graduation is customarily treated by finite difference formulas of great variety and complexity, these having been developed with the convenience of hand calculation in mind. The cheapening of computation which has occurred in the past few years permits a simplification and unification of the subject. This is accomplished by linear equations which express conditions it is desired to impose on the interpolating curve and the elimination of the constants resulting in a determinantal equation. A computer program which evaluates a determinant then suffices for nearly any problem of graduation, interpolation, numerical differentiation and integration, as well as for the calculation of the remainder term or error of any of these.