The Theory of Connections: Connecting Points Academic Article

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.

authors

• Mortari, Daniele

published proceedings

• MATHEMATICS

altmetric score

• 3

author list (cited authors)

• Mortari, D.

citation count

• 42

complete list of authors

• Mortari, Daniele

publication date

• January 2017

publisher

• MDPI  Publisher

published in

• MATHEMATICS  Journal

keywords

• Embedded Constraints
• Interpolation
• Linear Constraints

Digital Object Identifier (DOI)

• 10.3390/math5040057

start page

• 57

end page

• 57

volume

• 5

issue

• 4

URL

• http://dx.doi.org/10.3390/math5040057