Review Questions for Quiz #2

(Quiz #2 from the 2015 edition of the course is available here)

Conditions for applicability of the Weierstrass approximation theorem.

Construction of interpolating functions using approaches based on the Vandermonde matrix and Lagrange polynomials.

Construction of least-square fits for a given function or data.

Consider the problem of finding a polynomial interpolant to a given function f(x) defined on the interval [a,b]. What properties of this function do interpolation errors depend on?

For a given function f(x), how do the interpolation errors depend on the choice of the interpolation points?

Orthogonal polynomials: definition, examples, properties