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