A Linear Algebraic Approach to Teaching Interpolation‏

A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of the interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach enables the instructor to relate this topic to the topic of numerical solution of linear algebraic systems and, consequently, to introduce the important notion of stability. Finally, it is proposed to spice up the discussion of interpolation by describing its usage in cryptography for secret sharing.