Module 3 : Problem Discretization using Approximation Theory Section 4 : Discretization using Polynomial Interpolation 4 Discretization using Polynomial Interpolation
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چکیده
4 Discretization using Polynomial Interpolation Consider a function to be a continuous function defined over and let represent the values of the function at an arbitrary set of points in the domain Another function, say in that assumes values exactly at is called an interpolation function. Most popular form of interpolating functions are polynomials. Polynomial interpolation has many important applications. It is one of the primary tool used in the approximation of the infinite dimensional operators and generating computationally tractable approximate forms. In this section, we examine applications of polynomial interpolation to discretization. In the development that follows, for the sake of notational convenience, it is assumed that (84) 4.1 Lagrange Interpolation In Lagrange interpolation, it is desired to find an interpolating polynomial of the form (85) such that
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