Taking derivatives of numerical functions is one of the most often performed tasks in computation. Finite differences are a standard way to approximate the derivative of a function, and compact finite differences are especially attractive. We study the conditioning of differentiation, including some structured condition numbers for differentiation of polynomials. We look at differentiation matrices for derivatives of polynomials expressed in a Lagrange or Hermite interpolational basis. We look at regularization or smoothing before taking derivatives, and briefly touch on automatic differentiation.

No abstract

No abstract

No abstract

No abstract