Quasi-orthogonal Polynomials, Quadrature, and Interpolation

We investigate the quasi-orthogonal polynomials by expressing them as characteristic polynomials of symmetric matrices. Many properties of zeros of quasi-orthogonal polynomials are derived from this formulation. We derive new formulae for quadrature and interpolation based on the zeros of quasi-orthogonal polynomials and prove the mean convergence of Lagrange interpolation.