Algebraic hyperbolic spline quasi-interpolants and applications

In this paper, a construction of Marsden’s identity for UAH B-splines (i.e. Uniform Algebraic Hyperbolic B-splines) is developed and a clear proof is given. With the help of this identity, quasi-interpolant schemes that produce the space of algebraic hyperbolic functions are derived. Efficient quadrature rules, based on integrating some of these quasi-interpolant schemes, are constructed and studied. Numerical results that illustrate the effectiveness of these rules are presented.