The Theory of Connections: Connecting Points † Academic Article uri icon

abstract

  • © 2017 by the authors. This study introduces a procedure to obtain all interpolating functions, y = f (x), subject to linear constraints on the function and its derivatives defined at specified values. The paper first shows how to express these interpolating functions passing through a single point in three distinct ways: linear, additive, and rational. Then, using the additive formalism, interpolating functions with linear constraints on one, two, and n points are introduced as well as those satisfying relative constraints. In particular, for expressions passing through n points, a generalization of theWaring's interpolation form is introduced. An alternative approach to derive additive constraint interpolating expressions is introduced requiring the inversion of a matrix with dimensions equally the number of constraints. Finally, continuous and discontinuous interpolating periodic functions passing through a set of points with specified periods are provided. This theory has already been applied to obtain least-squares solutions of initial and boundary value problems applied to nonhomogeneous linear differential equations with nonconstant coefficients.

altmetric score

  • 3

author list (cited authors)

  • Mortari, D.

citation count

  • 19

publication date

  • November 2017