Orthogonal zero interpolants and applications‎

Orthogonal zero interpolants(OZI) are‎ ‎polynomials which interpolate the‎ ‎"zero-function"‎ ‎at a finite‎ ‎number of pre-assigned nodes and satisfy orthogonality condition‎. ‎OZIʹs can be constructed by the 3-term recurrence relation‎. ‎These‎ ‎interpolants are found useful in the solution of constrained‎ ‎approximation problems and in the structure of Gauss-type‎ ‎quadrature rules‎. ‎We present some theoretical and computational‎ ‎aspects of OZI?s and also discuss their structure and‎ ‎significance at the multiple nodes‎.