Quasiminimal reproducing quadratic spline interpolation (Q2714191)

The author investigates interpolation by quadratic splines at equidistant knots. Interpolation at the knots does not determine the spline uniquely. The remaining free parameter is specified by requiring a further condition which is different from the standard conditions known in the literature. For doing this the author introduces further so-called virtual knots outside the interval and uses the corresponding B-splines. Then the problem is to find the basis coefficients such that quadratic polynomials are reproduced and the norm of the coefficients satisfies a certain quasi-minimality condition. The author derives several formulas for computing the derivatives of the spline which determine the spline uniquely. It is shown that the method yields optimal approximation order.