A variational principle for a quadratic Hankel form

This chapter analyses a variational principle for a quadratic Hankel form. It describes the inversion of the Schrödinger or Krylov overlap matrix using a function defined by a scalar product in the Lanczos space. The variational principle shows that equating the derivatives of the function with respect to the polynomial expansion coefficients will immediately yield the result. Any determinant whose elements are signal points or power moments can be computed with analytical results. This has been demonstrated by Geronimus for a number of determinants that are otherwise difficult to compute numerically.